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• The phenomenon of periodic self-imaging of optical beams graded-index (GRIN) fibers was studied during the 1970s and was exploited to commercialize the GRIN lens. It has been found in recent years that the periodic self-imaging also affects the nonlinear propagation of optical pulses inside multimode GRIN fibers. • We present the theory of self-imaging in linear GRIN fibers using a modal expansion approach. It is shown that the optical field at any point inside the fiber can be written without any reference to the fiber modes as a two-dimensional integration over the input field using a propagation kernel that is similar to that found in diffraction theory. However, this kernel has a specific property that reproduces the input field precisely in a periodic fashion along the length of a GRIN fiber (self-imaging). • We apply this kernel to study the propagation of a Gaussian beam and discuss how self-imaging is modified by self-focusing produced by the Kerr nonlinearity. We then consider propagation of the continuous and pulsed Gaussian beams inside a GRIN fiber and discuss how self-imaging affects the modulation instability, leads to the formation of GRIN solitons, and produces novel temporal and spectral features when short optical pulses are launched that are intense enough to form high-order solitons. The phenomenon of periodic self-imaging of optical beams, occurring inside any graded-index (GRIN) medium, was studied during the decade of the 1970s and was exploited to commercialize the GRIN lens. It has been found in recent years that the periodic self-imaging also affects the nonlinear propagation of optical pulses inside multimode GRIN fibers. In this paper, we first present the theory of self-imaging in linear GRIN fibers using a modal expansion approach. It is shown that the optical field at any point inside the fiber can be written without any reference to the fiber modes as a two-dimensional integration over the input field using a propagation kernel that is similar to that found in diffraction theory. However, this kernel has a specific property that reproduces the input field precisely in a periodic fashion along the length of a GRIN fiber (self-imaging). We apply this kernel to study the propagation of a Gaussian beam and discuss how self-imaging is modified by self-focusing produced by the Kerr nonlinearity. We then consider propagation of the continuous and pulsed Gaussian beams inside a GRIN fiber and discuss how self-imaging affects the modulation instability, leads to the formation of GRIN solitons, and produces novel temporal and spectral features when short optical pulses are launched that are intense enough to form high-order solitons. [ABSTRACT FROM AUTHOR]

The complexity of residual toxic organics from biologically treated effluents of pulp and paper mills is a serious concern. To date, it has been difficult to choose the best treatment technique because each of the available options has advantages and drawbacks. In this study, two different treatment techniques using laboratory-scale aerobic sequencing batch reactors (SBRs) were tested with the same real recycled paper mill effluent to evaluate their treatment efficiencies. Two attached-growth SBRs using granular activated carbon (GAC) with and without additional biomass and a suspended-growth SBR were used in the treatment of real recycled paper mill effluent at a chemical oxygen demand (COD) level in the range of 800–1300 mg/L, a fixed hydraulic retention time of 24 h and a COD:N:P ratio of approximately 100:5:1. The efficiency of this biological treatment process was studied over a 300-day period. The six most important wastewater quality parameters, namely, chemical oxygen demand (COD), turbidity, ammonia (expressed as NH 3 –N), phosphorus (expressed as PO 4 3 –P), colour, and suspended solids (SS), were measured to compare the different treatment techniques. It was determined that these processes were able to almost completely and simultaneously eliminate COD (99%) and turbidity (99%); the removals of NH 3 –N (90–100%), PO 4 3 –P (66–78%), colour (63–91%), and SS (97–99%) were also sufficient. The overall performance results confirmed that an attached-growth SBR system using additional biomass on GAC is a promising configuration for wastewater treatment in terms of performance efficiency and process stability under fluctuations of organic load. Hence, this hybrid system is recommended for the treatment of pulp and paper mill effluents. [ABSTRACT FROM AUTHOR]

The rock–paper–scissors (RPS) game is known as one of the simplest cyclic dominance models. This game is key to understanding biodiversity. Three species, rock ( R ), paper ( P ) and scissors ( S ), can coexist in nature. In the present paper, we first present a metapopulation model for RPS game with mutation. Only mutation from R to S is allowed. The total population consists of spatially separated patches, and the mutation occurs in particular patches. We present reaction–diffusion equations which have two terms: reaction and migration terms. The former represents the RPS game with mutation, while the latter corresponds to random walk. The basic equations are solved analytically and numerically. It is found that the mutation induces one of three phases: the stable coexistence of three species, the stable phase of two species, and a single-species phase. The phase transitions among three phases occur by varying the mutation rate. We find the conditions for coexistence are largely changed depending on metapopulation models. We also find that the mutation induces different paradoxes in different patches. [ABSTRACT FROM AUTHOR]

The development of heat-induced antigen retrieval technologies with Tris-EDTA buffer has dramatically improved immunostaining of specific antigens for routine immunohistochemical detection (Krenacs et al., 2010) [1]. However, little evidence exists on whether heat-Induced antigen retrieval utilizing Tris-EDTA buffer can strip western blot (WB) membranes and allow sequential reprobing. Here, we serendipitously discover that ∼95 °C Tris-EDTA buffer with 0.01% Tween 20 could repeatedly strip the Nitrocellulose membranes (NC). After electroblotting, NC blots were soaked into Tris-EDTA stripping buffer (∼95 °C, 10–25min) and we could perform at least five rounds (the following antibodies used: Vinculin, Atg7, Caspase-3, UBA5, JNK and ERK1/2) stripping in sequential chemiluminescent detections. The NC membranes also show clear western signals and background without losing transferred proteins during the reprobing process of WB. Hence, this study report additional new roles of the heat-Induced antigen retrieval Tris-EDTA buffer with 0.01% Tween 20. The method is simpler, more affordable and harmless for the nitrocellulose paper, which will be helpful for effective reprobing in western blotting applications. [Display omitted] • We discover that heat-induced antigen retrieval technologies can strip the NC blots repeatedly up to 5 times. • Modified stripping protocol is composed of 0.1 M Tris, 0.01 M EDTA and 0.01% Tween-20 (pH 9.0–9.5). • The stripping buffer is easier and more efficient for probing different proteins. [ABSTRACT FROM AUTHOR]

The JK Paper industry located at Rayagada discharges biologically untreated effluent more than the permissible limit prescribed by Pollution Control Board, Odisha in to the environment. The industry is seriously polluting the surrounding aquatic and terrestrial environment. No detailed intensive study was carried out by previous workers on this industry earlier. The present study aims at finding out the impact of effluent on the flora at the contaminated site. The chemically treated effluent (TE) contained significant amount of mercury and cadmium. The TE has high BOD, COD, dissolved solids and suspended solids when compared to normal river water at the site of discharge. The TE deteriorated the natural water bodies changing the physico-chemical properties of natural river water. After meeting the river water the TE was diluted after 1 km distance from the meeting point of the river. Crop plants collected from the contaminated site showed higher level of residual Hg and Cd and significant depletion in pigment was observed. Plants collected from both the sides of the treated effluent canal showed significant amount residue mercury and cadmium in the plant leaves. The plants exposed to the TE, showed variation in chlorophyll and Phaeophytin pigment content when compared to their respective control values in all terrestrial plants collected from the contaminated site. In some plant leaves little increment in the pigment level was noted but the values were not significant. The changes observed in the plant pigment might be due to heavy metal accumulation. The presence of residual Hg and Cd in crop plants and plant leaves grazed by grazing animals after absorption, accumulation and enrichment may lead to a possible biological magnification, warrants attention. Proper biological treatment, treatment of effluent by modern methods and removal of heavy metals from the effluent before discharge by the industry is suggested. • Biological treatment of the effluent was not carried out by the industry & chemicals present in the effluent were significantly high.. • The water quality of the river water deteriorated due to the discharge of effluent of the paper mill. • Plants collected from the contaminated site showed significant accumulation of cadmium and mercury in leaf tissues • Significant depletion in pigment content of exposed plant leaves was noticed. • Depletion in plant pigment was due to accumulation of cadmium and mercury in plant tissues absorbed from the effluent. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Hypothesis The rate of stain growth of a sessile droplet deposited on paper has been previously studied (Kissa, 1981; Danino and Marmur, 1994; Kawase et al., 1986; Borhan and Rungta, 1993) but is not fully understood. In particular, the mechanism by which the abrupt decrease in growth rate occurs is unknown. This process is expected to follow a model where the disappearance of the droplet is represented by a change to the boundary condition at the droplet-paper interface when the volume of the fluid inside the paper is equal to the volume of the simulated droplet. Experiments The stain size of sessile droplets on paper was monitored against time. A series of fluids varying in surface tension and viscosity was studied. The kinetics of stain growth was modelled and compared with experiments and existing models of stain growth. Findings The measured stain area formed by a sessile droplet deposited on paper follows a two regime mechanism (Danino and Marmur, 1994). In the initial regime, the dynamics are governed by the filling of pores. However, in the later stage, the process is influenced by the emptying/redistribution of fluid. Simulations show that experimental results are well described by a model that identifies the change in boundary conditions after the droplet is no longer present above the paper, coupled with the change to a redistribution dominated mechanism. [ABSTRACT FROM AUTHOR]

Abstract The used methods in our papers [1–13] named new modified and extended auxiliary equation methods. The calculations of our article were correct. All solutions satisfied the partial differential equations in our papers. Highlights • The hydrodynamic mathematical methods. • We present nonlinear Schrodinger equation. • Solitary wave to the generalized nonlinear higher order of dynamical equation. • Fractional generalized reaction duffing equations. [ABSTRACT FROM AUTHOR]

Hypotheses (1) The equilibrium size and characteristics of a radially wicked fluid on porous material such as paper is expected to be dependent on the fluid properties and therefore could serve as a diagnostic tool. (2) The change in wicked stain size between biological fluids is dependent on a change in solid-liquid surface interfacial energy due to protein adsorption. Experiments Sessile droplets of increasing volume of blood, its components, and model fluids were deposited onto paper and the equilibrium stain size after coming to a halt was recorded. The contact angle of fluid droplets on model cellulose surfaces was measured to quantify the effect that blood protein adsorption at the solid-liquid interface has on radially wicked equilibrium size. Finally the significance of droplet evaporation for the time scale of interest was analysed. Findings The final stain area of all fluids tested on paper scales remarkably linearly with droplet volume. Different fluids were compared and the gradient of this linear relation was measured. Model fluids varying in surface tension and viscosity all behave similarly and exhibit a constant gradient. Blood and its components produce smaller stains, demonstrated by lower gradients. The gradient is a function of protein concentration, thus the mechanism of this phenomenon was identified as protein adsorption at the cellulose-liquid interface. The slope of the area/volume relationship for droplets is an important quantitative mechanistic variable. [ABSTRACT FROM AUTHOR]

This article describes a study on the viability of using waste from the paper industry: biomass boiler ash and green liquor dregs to fabricate mortars and concretes. Both types of ash were characterized by obtaining their chemical and mineralogical composition, their organic matter content, granulometry, adsorption and other common tests for construction materials. Seven different mortars were fabricated, one for reference made up of cement, sand, and water, three in which 10, 20, or 30% of the cement was replaced by biomass ash, and three others in which 10, 20, or 30% of the cement was replaced with dregs. Test specimens were fabricated with these mortars to conduct flexural and compression tests. Flexural strength is reduced for all the mortars studied. Compressive strength increases for the mortars fabricated with biomass ash and decreases for the mortar with dregs. Finally, 5 concretes were made, one of them as a reference (neither biomass ash nor dregs added), two of them with replacements of 10 and 20% of biomass ash instead of cement and another two with replacements of 10 and 20% of dregs instead of cement. The compressive and tensile splitting strength increase when a 10% of ash is replaced and decrease in all the other cases. The modulus of elasticity always decreases. [ABSTRACT FROM AUTHOR]

The removal of xenotrpic murine leukemia virus (xMuLV) by size-exclusion filter paper composed of 100% naturally derived cellulose was validated. The filter paper was produced using cellulose nanofibers derived from Cladophora sp. algae. The filter paper was characterized using atomic force microscopy, scanning electron microscopy, helium pycnometry, and model tracer (100 nm latex beads and 50 nm gold nanoparticles) retention tests. Following the filtration of xMuLV spiked solutions, LRV ≥5.25 log 10 TCID 50 was observed, as limited by the virus titre in the feed solution and sensitivity of the tissue infectivity test. The results of the validation study suggest that the nanocellulose filter paper is useful for removal of endogenous rodent retroviruses and retrovirus-like particles during the production of recombinant proteins. [ABSTRACT FROM AUTHOR]

Abstract Bisphenol A (BPA) is a high-production-volume chemical with endocrine disrupting properties commonly used as color developer in thermal paper. Concerns about the potential hazards of human BPA exposure have led to the increasing utilization of alternatives such as bisphenol S (BPS) and bisphenol F (BPF). This study was designed to assess: (i) BPA, BPS, and BPF concentrations in 112 thermal paper receipts from Brazil, France, and Spain by liquid chromatography coupled to mass spectrometry (LC-MS); and (ii) hormone-like activities of these receipts using two receptor-specific bioassays, the E-Screen for (anti-)estrogenicity and PALM luciferase assay for (anti-)androgenicity. BPA was present in 95.3% of receipts from Spain, 90.9% of those from Brazil, and 51.1% of those from France at concentrations up to 20.27 mg/g of paper. Only two samples from Brazil, two from Spain, and ten from France had a BPS concentration ranging from 6.46 to 13.29 mg/g; no BPA or BPS was detected in 27.7% of French samples. No BPF was detected in any receipt. Estrogenic activity was observed in all samples from Brazil and Spain and in 74.5% of those from France. Anti-androgenic activity was observed in > 90% of samples from Brazil and Spain and in 53.2% of those from France. Only 25.5% of French samples were negative for both estrogenic and anti-androgenic activity. Estrogenic and anti-androgenic activities per gram of paper were up to 1.411 µM estradiol (E 2) equivalent units (E 2 eq) and up to 359.5 mM procymidone equivalent units (Proceq), respectively. BPA but not BPS concentrations were positively correlated with both estrogenic and anti-androgenic activities. BPA still dominates the thermal paper market in Brazil and Spain, and BPS appears to be one of the main alternatives in France. There is an urgent need to evaluate the safety of alternatives proposed to replace BPA as developer in thermal printing. The large proportion of samples with hormonal activity calls for the adoption of preventive measures. Highlights • BPA or BPS but not BPF was present in nearly all thermal paper receipts. • Hormone-like activity was detected in > 80% of the receipts. • BPA levels were 30- to 100-fold higher than the EU-recommended level (0.2 mg/g). • BPS only appears to be an alternative to BPA in thermal paper from France. [ABSTRACT FROM AUTHOR]

The current study analyzed the high heating values (HHVs) of various waste biomass materials intending to the effective management and more sustainable consumption of waste as clean energy source. Various biomass waste samples including date leaves, date branches, coconut leaves, grass, cooked macaroni, salad, fruit and vegetable peels, vegetable scraps, cooked food waste, paper waste, tea waste, and cardboard were characterized for proximate analysis. The results revealed that all the waste biomass were rich in organic matter (OM). The total OM for all waste biomass ranged from 79.39% to 98.17%. Likewise, the results showed that all the waste biomass resulted in lower ash content and high fixed carbon content associated with high fuel quality. Based on proximate analysis, various empirical equations (HHV=28.296-0.2887(A)-656.2/VM, HHV=18.297-0.4128(A)+35.8/FC and HHV=22.3418-0.1136(FC)-0.3983(A)) have been tested to predict HHVs. It was observed that the heterogeneous nature of various biomass waste considerably affects the HHVs and hence has different fuel characteristics. Similarly, the HHVs of waste biomass were also determined experimentally using the bomb calorimeter, and it was observed that among all the selected waste biomass, the highest HHVs (21.19 MJ kg−1) resulted in cooked food waste followed by cooked macaroni (20.25 MJ kg−1). The comparison revealed that experimental HHVs for the selected waste biomass were slightly deviated from the predicted HHVs. Based on HHVs, various thermochemical and biochemical technologies were critically overviewed to assess the suitability of waste biomass to energy products. It has been emphasized that valorizing waste-to-energy technologies provides the dual benefits of sustainable management and production of cleaner energy to reduce fossil fuels dependency. However, the key bottleneck in commercializing waste-to-energy systems requires proper waste collection, sorting, and continuous feedstock supply. Moreover, related stakeholders should be involved in designing and executing the decision-making process to facilitate the global recognition of waste biorefinery concept. [Display omitted] • The high heating values (HHVs) of biomass waste were assessed with the aim for the sustainable consumption of waste as a source of clean energy. • All the biomass waste were rich in organic matter and fixed carbon content that ranged from 79.39% to 98.17% and 50.64%–54.26% respectively. • The maximum HHVs (21.19 MJkg−1) were recorded for cooked food waste. • The heterogeneous nature of various biomass waste considerably affects the HHVs and hence serve as suitable feedstock for various energy conversion technologies. [ABSTRACT FROM AUTHOR]

In the present study, plant-scale process integration was applied to an Indian paper mill using the water cascade analysis (WCA) technique. Three limiting constraints, chemical oxygen demand (COD), total dissolved solids (TDS), and adsorbable organic halides (AOX), were considered for the study. A nearest neighbor algorithm was used to distribute the freshwater and recycled water among the plant operations. It was found that the limiting critical constraint depends upon the types of processes and streams involved in the integration. The limiting critical constraint can differ for different sections of the same industry, and can differ in different schemes of integration. After process integration, a 55.6% reduction in effluent flow, a 36% reduction in COD, and a 73% reduction in AOX were observed. After process integration, a 35.21% reduction in pollution costs can be achieved and, assuming the average production of the mill to be 225 tons per day, a savings of Indian rupees (INR) 1.73 per kg of paper produced can be achieved by employing process integration. The water cess was calculated as INR 3024.77 per day without integration for the sections that were considered for integration, while after integration, a 41.53% savings in the form of water cess was calculated. [Copyright &y& Elsevier]

Highlights • We presented a metapopulation model with different victory rates in the rock-scissors-paper game. • We numerically obtained the solutions of reaction-diffusion equations on the graphs with two and three nodes. • We also analytically derived the approximate solutions of the equations. • When victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. • The heterogeneity of victory rates promoted the coexistence of species. Abstract Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species. [ABSTRACT FROM AUTHOR]

While the mate choice literature has focused primarily on the choices that females make, under certain circumstances males are expected to make mating decisions as well. Such circumstances include when males provide a significant energetic investment in a female or her offspring. Male orthopterans can invest considerable resources in females and have been studied for their mating investment decisions. However, while males provide acoustic information to females, females do not provide reciprocal acoustic information to males. Here, we tested the hypothesis that Laupala males use chemical signals to make mating decisions. We found that males and females have discernable differences in cuticular lipid expression when considering both whole-body and antennae-only extracts. Furthermore, access to the antennae alone resulted in males showing more courtship towards females and more aggressive behaviours towards males. Finally, males showed higher levels of association and courtship behaviour near female-exposed filter paper than they did near male-exposed and control filter paper. These results suggest that Laupala males use chemical signals when deciding whether to initiate courtship and open the possibility that chemical communication has played a role in the diversification of this genus. • Whole-body and antennae-only CHC expression differed in male and female Laupala. • Males spent more time near female antennae than male antennae. • Males tended to show courtship behaviour towards female antennae. • Males tended to show aggression towards male antennae. • Male courtship was elicited more often by female- than by male-exposed filter paper. [ABSTRACT FROM AUTHOR]

[Display omitted] Li-rich dual-phase Li-Cu alloy is a promising candidate toward practical application of Li metal anode due to its in situ formed unique three-dimensional (3D) skeleton of electrochemical inert LiCu x solid-solution phase. Since a thin layer of metallic Li phase appears on the surface of as-prepared Li-Cu alloy, the LiCu x framework cannot regulate Li deposition efficiently in the first Li plating process. Herein, a lithiophilic LiC 6 headspace is capped on the upper surface of the Li-Cu alloy, which can not only offer free space to accommodate Li deposition and maintain dimensional stability of the anode, but also provide abundant lithiophilic sites and guide Li deposition effectively. This unique bilayer architecture is fabricated via a facile thermal infiltration method, where the Li-Cu alloy layer with an ultrathin thickness around 40 μm occupies the bottom of a carbon paper (CP) sheet, and the upper part of this 3D porous framework is reserved as the headspace for Li storage. Notably, the molten Li can quickly convert these carbon fibers of the CP into lithiophilic LiC 6 fibers while the CP is touched with the liquid Li. The synergetic effect between the LiC 6 fibers framework and LiCu x nanowires scaffold can ensure a uniform local electric field and stable Li metal deposition during cycling. As a consequence, the CP capped ultrathin Li-Cu alloy anode demonstrates excellent cycling stability and rate capability. [ABSTRACT FROM AUTHOR]

This paper presents a simulation method that is used to study subcritical vibrations of a tube roll in a paper machine. This study employs asymmetric 3D beam elements based on the Timoshenko beam theory. An asymmetric beam model accounts for varying stiffness and mass distributions. Additionally, a detailed rolling element bearing model defines the excitations arising from the set of spherical roller bearings at both ends of the rotor. The results obtained from the simulation model are compared against the results from the measurements. The results indicate that the waviness of the bearing rolling surfaces contributes significantly to the subcritical vibrations while the asymmetric properties of the tube roll have only a fractional effect on the studied vibrations. [ABSTRACT FROM AUTHOR]

The amount of compostable bioplastics collected with the food waste is constantly growing, particularly due to the bags used for collection. According to the Italian legislation, compostable bioplastics must be accepted by all biological treatment plants, including aerobic and anaerobic facilities. Anyway, the compostability standard requires only the assessment of the aerobic degradability, while it is generally not required to test the behaviour under anaerobic conditions. This aspect is evaluated in the paper, where the anaerobic degradability of bioplastic bags used for the food waste collection is assessed. First, Biochemical Methane Potential (BMP) tests were performed on four commercial types of bioplastic bags, including those designed only for the collection of food waste and the shoppers, that can be reused for the same purpose. Subsequently, an innovative approach for this kind of substrate was applied, subjecting two bags to semi-continuous co-digestion tests together with the food waste. Both tests were performed by comparing the behaviour of bioplastic bags with that of an alternative collection paper bag. Finally, tests to evaluate the influence of physical phenomena on the degradation of bioplastics were performed to better understand the results of biological tests. BMP tests indicated a good degradability (>71%) of bioplastic bags, while semi-continuous tests showed a much lower degradability (<27%), confirmed by the observation of the undigested bag pieces. On the contrary, the paper bag presents interesting characteristics, because its degradability in the semi-continuous tests (82%) resulted even higher than that observed in the BMP tests (74%). These results highlight an important difference between the bags mono-digestion by means of BMP tests and the semi-continuous co-digestion tests with food waste, which better simulate the full-scale operational conditions. [Display omitted] • Bioplastic and paper bags were tested with BMP and semi-continuous digestion tests. • Paper bags show a good degradability in both the tests (>74%). • The BMP tests on bioplastic bags indicate a good degradability (>71%). • Semi-continuous digestion of bioplastics with food waste shows a low degradability. • The degradability of bioplastics is influenced by physical factors. [ABSTRACT FROM AUTHOR]

Abstract The pulp and paper industry is highly dependent on forest and water resources. It has more concerns on fair utilization of these resources and their conservation for its further expansion. Present study emphasizes on the use of rice straw (agro waste) in papermaking to protect wood based resources. It further deals with ozone bleaching (Z) prior to elemental chlorine free bleaching that proved to be significant in terms of reducing the effluent load specially the reduction in toxic, recalcitrant and carcinogenic compounds. Z based sequences resulted in pulp brightness of ∼85% that was 3.6% higher than the elemental chlorine free bleaching. Bleached pulps of Z based sequences were found to be having better strength properties than elemental chlorine based sequence and thus may be adopted as improved bleaching technology. The analysis of handsheets prepared after pulp bleaching was performed using X-Ray diffraction, ATR-FTIR and SEM. Incorporating ozone stage resulted in marked reduction of 58% and 63% in total solids in bleaching wastewater. Reduction of more than 80% in BOD, COD and adsorbable organic halides was achieved in Z based bleaching in comparison to chlorine bleaching. The amount of chlorophenols, guaiacols, catechols, vanillins and syringols became negligible (approx. 90% reduction) in effluents of Z based bleaching sequences. The chlorine dioxide followed by peroxide bleaching after Z stage was found to be the most promising to reduce the effluent load. Graphical abstract Image 1 Highlights • Ozone stage was incorporated prior to bleaching to reduce wastewater pollution. • Ozone based sequences showed higher brightness than conventional bleaching process. • Ozone bleaching showed better tensile and burst indices than elemental chlorine. • COD and BOD of bleaching effluent was reduced by 80% in ozone based sequences. • Chlorolignin compounds were reduced by 90% in effluent of ozone based sequences. [ABSTRACT FROM AUTHOR]

Abstract Environmental pollution due to various elements is increasing all across the planet owing to their use in industrial processes. The tobacco plants and the vegetables used in the manufacturing of smoking paper may accumulate these elements from the environment. Thus, tobacco and smoking paper may be relevant contributors among the content of elements in cigarettes, including some emerging pollutants such as rare earth elements (REEs). Thirty-two elements related to hi-tech industrial processes were analyzed in tobacco, rolling paper, and filters (n = 257 samples) by ICP-MS. A variety of industrial brands and "roll-your-own" cigarette papers were considered. The potential maximum daily exposure to these elements by a hypothetical heavy smoker was calculated for each type of cigarette. We found significant differences in the levels of most elements, both in the tobacco and in the paper. Black tobacco cigarettes contained the maximum levels. We found that the paper used in roll-your-own cigarettes may significantly modify their concentration of elements. Fast-burning, bleached, and flavored papers also contribute to higher levels of these pollutants. Thus, the differences in theoretical exposure depending on the type of cigarette consumed–either branded or hand-rolled–may be very striking, of up to 35–40 times. In addition to the number of cigarettes consumed per day, it is necessary to consider the type of cigarette consumed to assess the risk of exposure to toxic elements. Tobacco paper is a prominent source of exposure to toxic elements. Cigarette smoke is another source of exposure to emerging contaminants such as REE. Highlights • The type of cigarettes consumed influences the exposure to toxic elements. • Black tobacco cigarettes contain the highest concentrations of toxic elements. • The rolling paper may be a major contributor to the concentration of toxic elements released. • Cigarette consumption represents an additional source of exposure to rare earth elements. [ABSTRACT FROM AUTHOR]

Abstract A new method was employed to synthesize a novel high voidage ZIF-8 membrane over paper-like stainless steel fibers (PSSF). Firstly, paper-like stainless steel fibers (PSSF) were prepared by wet lay-up papermaking and sintering process, then the ZIF-8 membrane was coated on the PSSF support by secondary growth process. The effects of the seed layer growth time, the Hmim (2-methylimidazole)/Zn (Zinc nitrate hexahydrate) molar ratios, the solvothermal synthesis temperature and time on properties of ZIF-8 membrane/PSSF composites were investigated by modern characterization methods. The experimental results indicated that the void volume of ZIF-8 membrane/PSSF composites reached 89%. The optimal specific surface area of composites was 398 m2/g and the total pore volume was 0.174 cm3/g. Specifically, the size of seeds were approximately 250 nm when Hmim/Zn molar ratios and seed layer deposition time were 80 and 12 h, respectively. Under the condition of optimal seed layer, ZIF-8 membrane/PSSF composites showed outstanding continuity, compactness, free-defect and crystal shape when solvothermal synthesis time and solvothermal synthesis temperature were 24 h and 100 °C, respectively. Graphical abstract fx1 [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract In this work, we constructed a sensing system on Janus paper with hydrophilic side and hydrophobic side via depositing polymer precursor onto one side of qualitative filter paper. Water in humid environment (including liquid water, condensed moisture airflow and gaseous humid atmosphere) will be captured and gathered in the hydrophilic region of Janus paper due to the asymmetric hydrophobicity and hygroscopicity, which can induce the novel directional deformation. Additionally, MWCNTs (multiwalled carbon nanotubes) were loaded onto hydrophobic region beforehand to construct conductive network. The resistance of the conductive network changes synergistically as the Janus paper deforms in humid environment. Thus, the novel Janus paper realized the induction of environment humid factors, and conversion from the deformation signals to the desirable electric signals. The Janus paper also shows excellent stability in cycle use. [ABSTRACT FROM AUTHOR]

Abstract In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3]. The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order <2. [ABSTRACT FROM AUTHOR]

Abstract High-sensitivity C-reactive protein (hs-CRP) has been regarded as a risk predictor of cardiovascular disease (CVD). Despite there are many methods to detect hs-CRP, quantitative, rapid, convenient, multiplex and highly sensitive measurement of it is still a challenge for point-of-care applications. In this study, we developed a paper-based ELISA to detect hs-CRP and the sensitive chemiluminescence was applied as detection signal. In this developed assay method, CRP concentration and chemiluminescence intensity were linearly correlated (r = 0.999) with a limit of detection (LOD) as low as 0.49 ng mL−1, which was comparable to that of conventional ELISA and superior to most of the current reported POCT methods for detection of hs-CRP. The precision of the assay was confirmed for low coefficient of variations, less than 7% for intra-assay and less than 10% for inter-assay. In clinical sample analysis, the results of hs-CRP detected by this assay were in good accordance with which obtained by commercial high sensitivity ELISA kit for in vitro diagnosis (r = 0.975). This assay required only 4 μL of sample and could be finished in less than 30 min. It may therefore be employed as a rapid pre-screening tool to identify patients with elevated risk of CVD. Graphical abstract Image 1 Highlights • A chemiluminescence p-ELISA for detection of hs-CRP with the LOD of 0.49 ng mL−1. • Biotin-streptavidin system has been employed to improve the sensitivity of the assay. • Detection with less sample volume (4 μL) in shorter period of time (less than 30 min). • This assay has successfully detected hs-CRP in clinical serum samples. [ABSTRACT FROM AUTHOR]

Abstract With rapid growth of digital publishing, a great deal of document datum has been published online for a widely spread of knowledge innovations, which is an important resource for human survival and social development. However, it is a time-consuming and difficult task to conduct a high-efficiency access of valuable papers from an extremely large document database. A set of ranking techniques have been proposed to evaluate the influence of articles by counting the number and quality of citations, such as PageRank. In fact, the influence of an article does not merely depend on the account of citations, which is also highly related to the citation network. In this paper, we propose a visual analytics system for visual ranking of academic influence of articles, based on an insightful analysis of citation network. Firstly, a characterization of articles is established through word2vec model, based on an analogy between the articles in citation network and natural language processing (NPL) terms. Then, the difference between articles in the vectorized space is employed to optimize the PageRank model and achieve desired influence ranking results. A set of meaningful visual encodings are also designed to present the relationships among articles, such as the visualization of high-dimensional vectors and time-varying citation networks. At last, a visualization framework is implemented for visual ranking of academic influence of articles, with the ranking models and visual designs integrated. Case studies based on real-world datasets and interviews with domain experts have demonstrated the effectiveness of our system in the evaluation of academic influence of articles. [ABSTRACT FROM AUTHOR]

Enzyme-linked immunosorbent assay (ELISA) is an immunological assay commonly used to measure antibodies, antigens, proteins, and glycoproteins in biological samples. While the procedure is routine and straightforward, there are a number of variables (reagent selection, volume measurement, temperature, and time) that if not carefully considered, can affect the test outcome. Herein, we describe the development of microfluidic thread/paper-based analytical devices (µTPAD), microfluidic fabric-based analytical devices (µFAD), and microfluidic thread-based analytical devices (µTAD) as new platforms for ELISA. The quantitative detection of biotinylated goat anti-mouse IgG (system one) and rabbit IgG (system two) antibodies via colorimetric analysis is detailed. We explain the design and fabrication of the devices and the step-by-step protocol for the ELISA. A comparison between the techniques is described and the results obtained from them elucidated. [ABSTRACT FROM AUTHOR]

This article is an attempt to understand a mesh of complex relationships among tangible and intangible socio-economic factors that turned a desert city into the headquarters of one of the mighty polities in the Middle East in the fourteenth century CE. This paper argues that proto-industrialization led to the growth of 'virtual water' that helped the city of Yazd, in central Iran, to break free from its water limitation for the first time in its history. Yazd was almost absent in history until the twelfth century, as a peripheral oasis whose sparse population lived off subsistence agriculture irrigated by qanat systems (groundwater-mining subterranean channels). Following the Mongol invasion in the thirteenth century, the influx of landless refugees changed the relations of production and paved the way for proto-industrialization whose development hinged on skill and capital rather than water and land. Sufism and waqf (endowment tradition) contributed to the expansion of trading routes that facilitated the mobility of goods and people. The qanats were urbanized, and Yazd became an industrial hub where raw materials were processed into tradable products with considerable value added. This paper contributes to a broader understanding of the historical geography of the arid Middle East. • The Iranian city of Yazd rode out the Mongol invasion in the thirteenth century. • A surge of refugees upset the balance between population and agricultural resources. • Abundance of skilled workers led to a Middle Eastern mode of proto-industrialization. • Proto-industrialization engendered virtual water as an adaptation strategy. • Virtual water made a transition to a non-hydraulic society. [ABSTRACT FROM AUTHOR]

This paper discusses the re-animation of a geography departmental collection through a study of the archives and map collection of the School of Geography, University of Nottingham. The discussion is situated within parallel examples of work on geographical archives and map collections, and wider debates on engagement with archival sources. The paper considers how a previously dormant collection has been re-animated in recent years, conveys the range of source material involved, and discusses the possibilities of digitisation. The paper thereby raises questions which could be asked of the holdings of any academic department, from whatever time period. • The first detailed study of the re-animation of a geography departmental archival and map collection. • Shows a variety of original source material including photographic slides, plans, maps and posters. • Connects the study of a specific archive and map collection to wider debates on engagement with archival sources. • Examines the possibilities and implications of digitising analogue archival material. • Raises questions which could be asked of any archives and collections held by academic departments, from whatever period. [ABSTRACT FROM AUTHOR]

The paper investigates changes to Copenhagen's landscape of commemoration concerning its former colony, the Danish West Indies (DWI), prompted by the 2017 centennial anniversary of the Islands' sale to the US. It argues that Denmark, like other European nations, navigates a postcolonial identity crisis and that the landscape of commemoration plays a significant role within it. The paper advances our understanding of postcolonial Europe's identity crisis not only by shedding light on the under-explored case of Denmark, but also by emphasizing the role of the landscape of commemoration in this crisis. In addition to demonstrating how landscapes function as 'arenas' for negotiating expressions of hegemonic identity and territorial claims, it argues that the commemorative landscape is pivotal in tackling the construction of 'Europe' as a detached, self-made entity rather than a space (re)produced through connections with other (ed) places and people. It underscores that Europe's allegedly monochromatic historical fabric is woven from diverse global threads. Re-membering Europe with the people and regions vital to its (re)production re-writes them into European history and re-locates detached Europe (with)in the world. • Denmark can be situated within (post)colonial Europe's identity crisis. • Memories of the Danish West Indies are leveraged to negotiate Danish identity. • Copenhagen's commemorative landscape is instrumental in navigating the crisis. • Copenhagen's commemorative landscape redefines 'the Dane' and 'Denmark.'. [ABSTRACT FROM AUTHOR]

This paper examines the Linguistic Survey of India (LSI), a monumental exercise supervised by George Grierson to survey and classify the languages of colonial India. It considers why the LSI developed into an atypical scheme that corresponded with a multiethnic and multinational network of officials and scholars to survey India's languages. It makes the case that the networked practice of surveying was reciprocated at different scales, from localised linguistic surveys in districts and princely states to gather information and specimens, to a loosely governed transnational exercise involving Indians and Europeans to edit, review and publish results. The paper argues that the LSI's scalar geographies were negotiated by Grierson and, more importantly, his assistant Gauri Kant Roy and demonstrates that scale, as an analytic or process, was not an abstraction or predetermined for those entangled in the LSI's survey of India's languages. • Examines the Linguistic Survey of India from a historical geography perspective. • Highlights the LSI's uniqueness as a colonial Indian survey. • Draws on underutilised materials from National Archives of India. • Proposes a scalar and networked approach to the history of science and surveying. • Emphasises the significance of Gauri Kant Roy and various Indian surveyors in shaping India's linguistic geography. [ABSTRACT FROM AUTHOR]

Let X be a finite connected poset, K a field of characteristic zero and I (X , K) the incidence algebra of X over K seen as a Lie algebra under the commutator product. In the first part of the paper we show that any 1 2 -derivation of I (X , K) decomposes into the sum of a central-valued 1 2 -derivation, an inner 1 2 -derivation and a 1 2 -derivation associated with a map σ : X < 2 → K that is constant on chains and cycles in X. In the second part of the paper we use this result to prove that any transposed Poisson structure on I (X , K) is the sum of a structure of Poisson type, a mutational structure and a structure determined by λ : X e 2 → K , where X e 2 is the set of (x , y) ∈ X 2 such that x < y is a maximal chain not contained in a cycle. [ABSTRACT FROM AUTHOR]

Let k be an algebraically closed field of characteristic 0. We study some cohomological properties of Lie subalgebras of the Witt algebra W = Der (k [ t , t − 1 ]) and the one-sided Witt algebra W ≥ − 1 = Der (k [ t ]). In the first part of the paper, we consider finite codimension subalgebras of W ≥ − 1. We compute derivations and one-dimensional extensions of such subalgebras. These correspond to Ext U (L) 1 (M , L) , where L is a subalgebra of W ≥ − 1 and M is a one-dimensional representation of L. We find that these subalgebras exhibit a kind of rigidity: their derivations and extensions are controlled by the full one-sided Witt algebra. As an application of these computations, we prove that any isomorphism between finite codimension subalgebras of W ≥ − 1 extends to an automorphism of W ≥ − 1. The second part of the paper is devoted to explaining the observed rigidity. We define a notion of "completely non-split extension" and prove that W ≥ − 1 is the universal completely non-split extension of any of its subalgebras of finite codimension. In some sense, this means that even when studying subalgebras of W ≥ − 1 as abstract Lie algebras, they remember that they are contained in W ≥ − 1. We also consider subalgebras of infinite codimension, explaining the similarities and differences between the finite and infinite codimension situations. Almost all of the results above are also true for subalgebras of the Witt algebra. We summarise results for W at the end of the paper. [ABSTRACT FROM AUTHOR]

This paper presents an extension of Bhargava's theory of factorials associated to any nonempty subset S of Z. Bhargava's factorials k ! S are invariants, constructed using the notion of p -orderings of S where p is a prime. This paper defines b -orderings of any nonempty subset S of Z for all integers b ≥ 2 , as well as "extreme" cases b = 1 and b = 0. It defines generalized factorials k ! S , T and generalized binomial coefficients ( k + ℓ k ) S , T as nonnegative integers, for all nonempty S and allowing only b in T ⊆ N. It computes b -ordering invariants when S is Z and when S is the set of all primes. [ABSTRACT FROM AUTHOR]

Paul Erdos and Carl Pomerance have proofs on an asymptotic upper bound on the number of preimages of Euler's totient function ϕ and the sum-of-divisors functions σ. In this paper, we will extend the upper bound to the number of preimages of iterates of ϕ and σ. Using these new asymptotic upper bounds, a conjecture in de Koninck and Kátai's paper, "On the uniform distribution of certain sequences involving the Euler totient function and the sum of divisors function" is now proven and many corollaries follow from their proven conjecture. [ABSTRACT FROM AUTHOR]

The rational fertilisation of olive trees, based on adding exclusively the nutrients that are actually needed, is important from both the economic and environmental sustainability points of view. This paper employs UAV-obtained multispectral data collected from five different orchards located in Southern Spain to build a set of models for the prediction of the leaf nutrient content of olive trees using Support Vector Regression. The paper shows the convenience of addressing the problem as a Multiple Instance Regression, and compares two strategies of data aggregation and different choices of feature vectors derived from the raw multispectral data. The models provided good results for N, P and K (r 2 = 0.76, r 2 = 0.87 and r 2 = 0.91, respectively for the Hojiblanca model, and r 2 = 0.79, r 2 = 0.80 and r 2 = 0.80 for the Picual model). The rest of nutrients studied also offered good results for both the Picual and Hojiblanca models, ranging from r 2 = 0.69 for B to r 2 = 0.93 for Cu. The results indicate a robust performance of the models and a potential for improvement with the addition of more data, along with an advantage of considering individual models for each cultivar variety. Overall, these results are very promising for the estimation of the leaf nutrient content of olives trees and the detection of spatial variability in the fertilisation needs of orchards. [Display omitted] • Leaf nutrient content of olive trees is predicted from UAV multispectral data. • Multiple Instance Regression is applied and its benefits discussed. • Models provide good results for N, P and K in the Hojiblanca and Picual models. • The rest of nutrients also show acceptable results. • Results are promising for detecting spatial variability in fertilisation needs. [ABSTRACT FROM AUTHOR]

We provide generalizations of a class of stochastic Gronwall inequalities that has been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This class of stochastic Gronwall inequalities is a useful tool for SDEs. Our focus are convex generalizations of the Bihari-LaSalle type. The constants we obtain are sharp. In particular, we provide new sharp constants for the stochastic Gronwall inequalities. The proofs are connected to a domination inequality by Lenglart (1977), an inequality by Pratelli (1976) and a characterization of Lenglart's concept of domination via the Snell envelope. The inequalities we study appear for example in connection with exponential moments of solutions to path-dependent SDEs: For non-path-dependent SDEs, criteria for the finiteness of exponential moments are known. To be able to extend these proofs to the path-dependent case, a convex generalization of a stochastic Gronwall inequality seems necessary. Using the results of this paper, we obtain a criterion for the finiteness of exponential moments which is similar to that known for non-path-dependent SDEs. Stochastic Gronwall inequalities can also be applied to study other types of SDEs than path-dependent SDEs: An estimate of this paper is applied by Agresti and Veraar (2023) to prove global well-posedness for reaction-diffusion systems with transport noise. [ABSTRACT FROM AUTHOR]

In 1935, the introduction of the norm of a group by Reinhold Baer is a turning point in group theory. In fact, Baer proved that there is a very strong relationship between the structure of the norm and that of the whole group (see [1] , [2] , [3] , [4] , [5]). Since then, the norm has been playing a very significant roles in many aspects of group theory and its applications: it has been used in [43] to describe the connection between Hopf–Galois structures and skew braces; it has been used in [23] to describe some special types of profinite groups; and it has been fundamental in the theory of subgroup lattices of groups (see [40]). In this paper, we weaken the original definition of norm by taking into account only those subgroups that are "large" in some sense. Depending on the chosen concept of largeness, the resulting norm can have an impact on the structure of the whole group that is even greater than that of Baer's norm. This is exactly what happens with the non-polycyclic norm , and in fact, Theorem 4.17 gives a precise description of generalized soluble groups in which the non-polycyclic norm is non-Dedekind (and can be considered as the main result of the paper). Other times, the resulting norms have their own peculiar behaviour; this is the case if "large" means "infinite", "having infinite rank", "being non-Černikov", or "having cardinality m " for some given uncountable cardinal number m. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following elliptic system of Hamiltonian type on a bounded domain: (0.1) { − Δ u = K 1 (| y |) | v | p − 1 v , in B 1 (0) , − Δ v = K 2 (| y |) | u | q − 1 u , in B 1 (0) , u = v = 0 on ∂ B 1 (0) , where K 1 (r) and K 2 (r) are positive bounded functions, B 1 (0) is the unit ball in R N , (p , q) is a pair of positive numbers lying on the critical hyperbola: 1 p + 1 + 1 q + 1 = N − 2 N. We investigate the local uniqueness and the nondegeneracy of the bubbling solution for problem (0.1). Our proof is based on the local Pohozaev identities, blow-up analysis, and the properties of Greens function. Our results are quite different from single equation, which is mainly caused by the non-cooperative nonlinear terms and (p , q) lying on the critical hyperbola. We believe that the various new ideas and technique computations that we used in this paper would be very useful to deal with other related problems of Hamiltonian type with interact critical exponents. [ABSTRACT FROM AUTHOR]

In this paper, we study the following (p , q) -Laplacian equation with L p -constraint: { − Δ p u − Δ q u + λ | u | p − 2 u = f (u) , in R N , ∫ R N | u | p d x = c p , u ∈ W 1 , p (R N) ∩ W 1 , q (R N) , where 1 < p < q < N , Δ i = div (| ∇ u | i − 2 ∇ u) , with i ∈ { p , q } , is the i -Laplacian operator, λ is a Lagrange multiplier and c > 0 is a constant. The nonlinearity f is assumed to be continuous and satisfying weak mass supercritical conditions. The purpose of this paper is twofold: to establish the existence of ground states, and to reveal the basic behavior of the ground state energy E c as c > 0 varies. Moreover, we introduce a new approach based on the direct minimization of the energy functional on the linear combination of Nehari and Pohozaev constraints intersected with the closed ball of radius c p in L p (R N). The analysis developed in this paper allows to provide the general growth assumptions imposed to the reaction f. [ABSTRACT FROM AUTHOR]

This paper concerns static and evolution equations involving degenerate curls. The topic is motivated by the mathematical problems of Meissner states of anisotropic superconductors, and of the nonlinear magneto-static Maxwell equations with strong anisotropy. Two types of degenerate curls are studied, among them one is the directional curl along a unit length vector field, which has been introduced by the author before, and the other is the matrix-curl, which is introduced in this paper. Because of the degeneracy produced by the degenerate curl of the unknown vector field in the leading term of the equation, the boundary condition should be prescribed on part of the boundary according to the nature of the degenerate curl. We formulate the Dirichelt type and natural type boundary conditions, and give existence of solutions both for the static equations and for the evolution equations. [ABSTRACT FROM AUTHOR]

This article is the final one in the series of papers by the authors devoted to finite-dimensional singular (simple right-alternative with zero product in the even part) superalgebras. In previous papers, algebraically generated singular superalgebras were studied and it was proved that any such superalgebra has the structure of an extended double. In this article, we prove that any singular superalgebra is algebraically generated and, therefore, has the structure of an extended double. [ABSTRACT FROM AUTHOR]

The paper examines information structures that can guarantee full surplus extraction via collusion-proof mechanisms. Our collusion-proofness notion requires that there does not exist any coalition whose manipulation can affect the mechanism designer's payoff. When the mechanism designer is restricted to using standard Bayesian mechanisms, we show that under almost every prior distribution of agents' types, there exist payoff structures under which there is no collusion-proof full surplus extracting mechanism. However, when ambiguous mechanisms are allowed, we provide a weak necessary and sufficient condition on the prior such that collusion-proof full surplus extraction can be guaranteed. Thus, the paper sheds light on how the collusion-proofness requirement resolves the full surplus extraction paradox of Crémer and McLean (1985, 1988) and how engineering ambiguity in mechanism rules restores the paradox. [ABSTRACT FROM AUTHOR]

In a previous paper (Feng et al., J. Differential Equations (2023)), we studied a seasonally interactive model between closed seasons and open seasons with Michaelis-Menten type harvesting, in which we assumed that the harvesting quantity was relatively large (0 < κ = l G c E < 1) and obtained a length threshold of the closed season T ¯ ⁎ depending on the harvesting parameter and the seasonal fluctuation period. It was shown that the origin is globally asymptotically stable if and only if T ¯ ≤ T ¯ ⁎ , and there exists a unique globally asymptotically stable T -periodic solution if and only if T ¯ > T ¯ ⁎. In this paper, we continue to investigate the periodic dynamics of this model when the harvesting quantity is relatively small (κ = l G c E ≥ 1). By finding another smaller length threshold T ¯ ⁎ ∈ (0 , T ¯ ⁎) , we determine the number of periodic solutions and study their stability, which imply the occurrence of bifurcation of periodic solutions. Our results demonstrate that designing the closed harvesting season properly can prevent the species from extinction. Moreover, by comparing with the continuous harvesting model and combining the results in our previous paper and this article, we provide a complete understanding on the global dynamics for the periodic switching model. Some numerical simulations are also carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Ordinary and partial differential equations with operators containing the p -Laplace operator, the so called ϕ -Laplace operator, operators with variable exponents and the double phase operators have been studied thoroughly for at least the last 20 years and the amount of papers dealing with these subjects is huge. In this paper we deal with the problem of the existence of periodic solutions to some system of ODE's involving a fairly general operator generalizing in this form corresponding results for the areas of research just mentioned. In our results neither the function generating the differential operator nor the right hand side function in the boundary value problem considered are necessarily equal to the gradient of a function. Our main result is a here is a continuation theorem based on the Leray-Schauder degree theory which allows us to obtain the existence of solutions for the boundary value problem considered. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of planar viscous shock wave for the 3-dimensional compressible Navier-Stokes-Poisson (NSP) system in the domain Ω : = R × T 2 with T 2 = (R / Z) 2. The stability problem of viscous shock under small 1-dimensional perturbations was solved in Duan-Liu-Zhang [7]. In this paper, we prove the viscous shock is still stable under small 3-d perturbations. Firstly, we decompose the perturbation into the zero mode and non-zero mode. Then we can show that both the perturbation and zero-mode time-asymptotically tend to zero by the anti-derivative technique and crucial estimates on the zero-mode. Moreover, we can further prove that the non-zero mode tends to zero with exponential decay rate. The key point is to estimate the non-zero mode of nonlinear terms involving electronic potential, see Lemma 6.1 below. [ABSTRACT FROM AUTHOR]