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In this paper, several Kaczmarz-type numerical methods for solving the matrix equation $AX=B$ and $XA=C$ are proposed, where the coefficient matrix $A$ may be full rank or rank deficient. These methods are iterative methods without matrix multiplication. Theoretically, the convergence of these methods is proved. The numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrices., Comment: arXiv admin note: text overlap with arXiv:2305.16684

In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the convergence rate and some convergence conditions including the case that the coefficient matrix is rank deficient. By varying three parameters in the new method and convergence theorems, the new method recovers an array of well-known algorithms and their convergence results. Meanwhile, with the use of Gaussian sampling, we can obtain the Gaussian global randomized Kaczmarz (GaussGRK) method which shows some advantages in solving the matrix equation AXB = C. Finally, numerical experiments are given to illustrate the effectiveness of recovered methods., Comment: arXiv admin note: text overlap with arXiv:1506.03296, arXiv:1612.06013, arXiv:2204.13920 by other authors

In this study, we synthesized nano-microemulsions of calcium carbonate (CaCO3)-encapsulated curcumin (Cur)-Ferulic acid (FA) ester derivatives of diverse mass ratios by using the solution casting approach. The structures, antioxidant and antimicrobial activities, physical properties, and potential of hydrogen (pH) sensitivity of these products were examined. Compared with microparticles of CaCO3, those of CaCO3@Cur-FA exhibited excellent antimicrobial and antioxidant properties. Response to pH was indicated through the release of Cur-FA from CaCO3@Cur-FA in solutions having different pH values. The results demonstrated that Cur-FA was released more quickly from CaCO3@Cur-FA at pH 5.5 than at pH 7.4. CaCO3@Cur-FA demonstrated good antioxidant capacities through its ability to scavenge 2,2′-amino-di(2-ethyl-benzothiazoline sulphonic acid-6)ammonium salt (ABTS+) and 1,1-diphenyl-2-picrylhydrazyl (DPPH). These activities were three-fold more than those observed in CaCO3 microparticle control groups; additionally, the antimicrobial activity against Aspergillus niger and Escherichia coli increased by 40.5 and 54.6%, respectively. Overall, the microparticles of CaCO3@Cur-FA outperformed Cur-FA in terms of antimicrobial properties by inhibiting the growth of certain zoonotic pathogens.

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Additional file 6: All additional figures.

Fast and reliable localization of high-energy transients is crucial for characterizing the burst properties and guiding the follow-up observations. Localization based on the relative counts of different detectors has been widely used for all-sky gamma-ray monitors. There are two major methods for this counts distribution localization: $\chi^{2}$ minimization method and the Bayesian method. Here we propose a modified Bayesian method that could take advantage of both the accuracy of the Bayesian method and the simplicity of the $\chi^{2}$ method. With comprehensive simulations, we find that our Bayesian method with Poisson likelihood is generally more applicable for various bursts than $\chi^{2}$ method, especially for weak bursts. We further proposed a location-spectrum iteration approach based on the Bayesian inference, which could alleviate the problems caused by the spectral difference between the burst and location templates. Our method is very suitable for scenarios with limited computation resources or time-sensitive applications, such as in-flight localization software, and low-latency localization for rapid follow-up observations.

Water lubrication has gradually replaced oil lubrication for a wide range of marine stern bearings. However, due to poor water carrying capacity, the tribological performances of water lubricated bearings can be improved by incorporating surface textures. In this work, rhombic textured thermoplastic polyurethane (TPU) specimens, 3D-printed with different heights/depths, 1 mm bulge, 0.5 mm bulge, 0.5 mm dimple, and 1 mm dimple, were tested for their tribological performances when they were lubricated by water and were compared to nontextured specimens. The friction coefficient, wear mass, and microscopic surface topography of the specimens were collected at a common working load (0.4 MPa) and speed (from 50 to 350 rpm), and at low-speed and heavy load (50 rpm and 0.8 MPa) conditions. Experimental results reflect that the rhombic surface texture can effectively improve the friction and wear performances of TPU materials. The friction coefficients of most textured specimens are smaller than those of non-textured specimens under various working conditions. The surface wear conditions of all textured specimens are superior to non-textured specimens, since the rhombic surface texture produces additional hydrodynamic lubrication by creating converge and cavitation effects and prevents abrasive particles from accumulating on the friction surface. Through experimental demonstration, the 1 mm bulge rhombic texture is the best of all the tested textured specimens. This finding can provide a reference for practical industrial applications.

Asymmetric casings filled with explosive have attracted increasing attention in innovative warhead design (e.g. aimable warhead) and improvised explosive device protection. Previous research showed that greater damage could be realized to the target with the fragment cluster from multiple fragment layers than from a single fragment layer. As a typical asymmetric casing, D-shaped casing has been used in deformable aimable warhead, deployable aimable warhead as well as warhead in hypersonic weapons. To assist in the design of asymmetric warhead, this work examined the velocity distribution and impact performance of fragments cluster from the D-shaped casing with multiple fragment layers. The fragment velocity distribution and fragment dispersion of the D-shaped casing with different fragment layers were experimentally analyzed. In addition, the effects of fragment layer on the distribution of fragment velocity were analyzed by comparing theoretical model and experimental results. Experimental and theoretical analysis showed significant energy dissipation from the collision and friction between fragments, and the dissipated energy increased obviously with rising number of fragment layers. The findings herein could serve as a reference for further investigations of multi-layer fragment structures and provide a foundation for asymmetric warhead design.

The axial pump operating in the pump-as-turbine mode is a practical and cost-saving alternative suitable for low-head pico hydropower in rural and remote areas that bypasses the need for expensive turbines. Their pump characteristics, however, indicate that efficiency is low in off-design flow rates. Using the computational fluid dynamics, the adjustable inlet guide vanes with five angles (±20°, 0°, ±10°) in front of the impeller of the axial pump have been redesigned and installed specifically to increase the operating range of high efficiency in the pump-as-turbine mode. To validate the simulation method, a prototype of the axial pump was built to measure in the pump mode the pump characteristics including head and efficiency. The results obtained show that the computational fluid dynamics calculated results are in qualitative agreement with the experimental data. In the pump-as-turbine mode, the adjustable inlet guide vanes were found to affect the performance of the axial pump. The most important aspect is that the adjustable inlet guide vanes widen the efficiency range if the inlet guide vane angle is adjusted for different flow rates. For the same situation with negative angles, the efficiency values at the BEP are higher than those with positive angles, where the efficiency around the angle − 10° is the highest. The main reason is that the direction of flow at the impeller-zone exit is guided by the adjustable inlet guide vanes to reduce the energy loss, which can be supported in the view of vector field and energy losses of different parts of pump.

The application of wave guide vanes with bio-inspired leading-edge protuberances to the hump characteristic of a pump-turbine is examined in this study. Numerical simulation with a shear-stress transport turbulence model is used to calculate the three-dimensional flow in a pump-turbine in pumping mode. Three tubercle amplitudes of 0.02c, 0.04c, and 0.08c (c is chord length), and three spanwise wavenumbers (2/s, 4/s and 8/s, s is the length of span) for guide vanes are especially considered. The results obtained show that the simulated performances of original guide vanes are found to be in good qualitative agreement with experimental data, supporting the validation of the computational fluid dynamics method. For different wave guide vanes with leading-edge protuberances, it is shown that the hump characteristic of the pump-turbine in pumping mode is effectively improved. This is due to improved flow fields below the tongue in view of entropy production and vector field. The energy loss can be clearly compared through the entropy distribution for different locations of the guide vanes, and it is improved for the wave guide vanes with bio-inspired leading-edge protuberances. For current pump-turbine, the optimal amplitude and wavenumber are found to be around 0.04c and 4/s.

Eccentric initiation is an innovative design for warheads, by which warheads are detonated off-axis. The effects of eccentric initiation have been well studied. However, it has been found that the experimental and numerical results of the circumferential distribution of fragment velocity under eccentric initiation are inconsistent, yet no rational explanation has been reported. In the present work, the influence of axial rarefaction waves on the eccentric effect was numerically studied as a major factor for such an inconsistency. The circumferential fragment velocity distributions of the cylindrical casings filled with explosives with different length-diameter ratios (L/D) under eccentric initiation were numerically studied. The results indicate that axial rarefaction waves affect the acceleration process of fragments, and subsequently influence the effect of eccentric initiation. The axial fragment velocity distributions of the casings with different numbers of end caps were measured with X-ray radiography to explore the axial rarefaction wave suppressing performance of end caps. The experimental results indicate that end caps can significantly suppress the effects of axial rarefaction waves. Our work has provided a scientific foundation for the studies on eccentric initiation and engineering design of innovative warheads.

When an electricity meter is calibrated under the condition of non-reference temperature, it is generally necessary to correct the verification result according to the actual temperature of the verification environment, and then judge whether the electricity meter is qualified. Under the mode of large-scale automatic verification, the space of workplace can reach thousands of square meters, and the temperature distribution is uneven. In order to reduce the cost of controlling verification environment temperature, the effort of trying to broaden the range of verification environment temperature has been always made by researchers. The problem is that it is difficult to make an effective judgment on the batch verification results based on the verification data. Under this circumstance, a data analysis method which helps to ensure weather the verification results are effective is needed. In this paper, the batch electricity meters verification experiment is designed and carried out firstly, then the distribution characteristics of verification data are studied, and the conclusion is obtained that the distribution type of verification data is normal distribution. On this basis, the method based on parameter test is used to analyze the data consistency, which shows that this data analysis method can make auxiliary evaluation on the validity of verification data produced in non-reference temperature environment. The data analysis method described in this paper can be applied to the operation state evaluation of large-scale automatic verification system and can also provide data analysis means for broadening the range of environment temperature for large-scale automatic verification.

In order to ensure the safe and stable operation of the power supply system, an online fault detection method based on local features of data is proposed for the loop network cabinet data modeling and online monitoring. Using the strategy of local feature extraction based on neighborhood preserving embedding (NPE) algorithm, real-time data features are obtained through multiple measurement variable information and environment variable information of ring network cabinet, and a fault detection model of ring network cabinet based on data features is constructed. The constructed NPE model is applied to the on-line detection of real ring network cabinet, and the original data space is divided into irrelevant feature space and data residual space. According to these two spaces, the monitoring statistics of Hotelling T 2 and the sum of the squared prediction errors (SPE) are constructed respectively, and based on these two monitoring statistics, the online real-time monitoring and fault alarm of ring network cabinet are realized. This method is applied to the fault detection of ring network cabinet, and the test results prove the effectiveness of this method in fault detection of ring network cabinet.

Stimuli-responsive micro/nanostructures that can dynamically and reversibly adapt their configurations according to external stimuli have stimulated a wide scope of engineering applications, ranging from material surface engineering to micromanipulations. However, it remains a challenge to achieve a precise local control of the actuation to realize applications that require heterogeneous and on-demand responses. Here, a new experimental technique is developed for large arrays of hybrid magnetic micropillars and achieve precise local control of actuation using a simple magnetic field. By manipulating the spatial distribution of magnetic nanoparticles within individual elastomer micropillars, a wide range of the magnetomechanical responses from less than 5% to ≈50% for the ratio of the bending deflection to the original length of the pillars is realized. It is demonstrated that the micropillars with different degrees of bending deformation can be configured in any spatial pattern using a photomask-assisted template-casting technique to achieve heterogeneous, site-specific, and programmed bending actuations. This unprecedented local control of the micropillars offers exciting novel applications, as demonstrated here in encryptable surface printing and stamping, direction- and track-programmable microparticle/droplet transport, and smart magnetic micro-tweezers. The hybrid magnetic micropillars reported here provide a versatile prototype for heterogeneous and on-demand actuation using programmable stimuli-responsive micro/nanostructures.

The spatially confined evanescent microwave photonics have been proved to be highly desirable in broad practical scenarios ranging from robust information communications to efficient quantum interactions. However, the feasible applications of these photonics modes are limited due to the lack of fundamental understandings and feasible directional coupling approaches at sub-wavelengths. Here, we experimentally demonstrate the efficient near-field photonic routing achieved in waveguides composed of two kinds of single-negative metamaterials. Without mimicking the polarization features, we propose all-electric near-field metasource in subwavelength scale and exemplify its near-field functions like Janus, Huygens and spin sources, corresponding to time-reversal, parity-time and parity symmetries of its inner degree of freedom. Our work furthers the understandings about optical near-field symmetry and feasible engineering approaches of directional couplings, which would pave the way for promising integrated mircrowave photonics devices., Comment: 6 pages, 4 figures

The magnetic shield plays an important role in magnetic near-field control. However, the requirements of efficient, ultrathin, lightweight and cheap are still the challenges. Here, we firstly propose a composite metamaterial in which the mu-near-zero media is covered with a ferrite slab. We verify that this structure can enhance the shielding effectiveness in a small area. Furthermore, we optimize the magnetic path by changing the bulk ferrite slab into a patterned slab. In this way, significant shielding effectiveness enhancement can be achieved in a large area. Experimental results show that the maximum shielding effectiveness (SE) of the composite metamaterial with a patterned ferrite is 20.56 dB, which is nearly 19 dB higher than that of a single ferrite slab with the same thickness of the composite metamaterial. The results on the composite metamaterial would be very useful in the applications involving magnetic shielding., Comment: 5 pages, 5 figures

In this work, we treat the rotation of the optical axis as a new degree of freedom and theoretically propose a tilted linear-crossing metamaterials (TLCMM). Specifically, the conical dispersions of the NLCMM and TLCMM have the same shapes as type-I and type-II Dirac cones, respectively, in condensed matter physics. Upon rotating the optical axis angle such that it is equal to the cone angle, we find that this special TLCMM has the shape of a type-III Dirac cone. This critical TLCMM can have many unique properties and is of a fundamentally different nature than neighboring phases. When EM waves with large wave vectors are incident to a metamaterial with an open IFC to free space, the incident EM wave is strongly reflected due to wave-vector mismatch. Here, we use boundary conditions and the causality law to reveal that TLCMM high-k modes can achieve abnormal refraction without reflection and filtering. Moreover, these phenomenon are observed experimentally in a planar circuit-based system. The circuit-based TLCMM not only provides a versatile platform for the study of robust negative refraction phenomena in metamaterials, but also has a planar structure that is easier to integrate. Our results regarding the manipulation of EM waves may enable their use in planar-integrated photonics including for directional propagation, cloaking, and switching., Comment: 29 pages, 7 figures

In this paper, a novel optical inspection apparatus was studied which enables one to inspect both top and bottom surfaces of the thermoelectric cooler (TEC) components. In the optical inspection apparatus, a right angle prism reflector located beneath the glass stage was used to image the bottom surface of the TEC component on top of the stage. In order to obtain the clear images of two surfaces of the TEC component simultaneously, a proper telecentric imaging lens with sufficient large depth of field needs to be selected to address their optical path difference. A telecentric optical imaging lens DH110-03F50 with depth of field of around 6mm together with a right angle prism reflector with solpe side length of 3.6mm was chosen for this experimental setup. With this apparatus three groups of components were inspected in the experiments and each group has some typical samples with specially selected Passed and Failed features on the surfaces to be examined. The experimental results indicate that the images of both top and bottom surfaces obtained using the optical inspection system are sufficiently clear and well resolved which meets the requirements for the following image processing. The results show that the proposed technique allow us to inspect both top and bottom surfaces of the component with simplified configuration and effective cost. This novel inspecting technique will find applications in the automatic optical inspection systems for the TEC components.

With the technical development of new warhead designs and explosive protection, theoretical research on the velocity distribution along the axis is important. The velocity distribution of fragments along the axis of 2 kinds of non-cylindrical casings, which were detonated at one end, was obtained and investigated in this paper with a flash-radiograph technique. The results of the experiments indicated that the rarefaction wave generated at 2 ends of the non-cylindrical casings was only related to the diameter of the explosive, instead of the filled ratio. According to the experimental conclusion, an “extended hard core” model was proposed, and its parameters were determined based on the analysis of the velocity distribution of different kinds of explosive-filled casings. This formula is able to directly obtain the velocity distribution of the non-cylindrical casing, which was detonated at one end, without needing experiments to determine unknown parameters. The formula is highly accurate and has a wide range of applications, which provides the basis for the new engineering design of diverse conventional warheads and explosive protection structure.

Compared with the traditional air spraying technique and electroplate method, the coating defects of bonded NdFeB magnet, such as the workpiece hanging point, the pinhole, the bubble, have been solved by using the composite powder electrostatic spraying as surface treatment technology, along with the EE epoxy paint as primer coating and PU polyurethane paint as surface coating. The coating of this composite powder electrostatic spraying is uniform and compact, and the coating has strong adhesion and corrosion resistance. This paper gives a detailed introduction to the composite powder electrostatic spraying, including the choice of some important parameters and the unique hanging tools of composite powder electrostatic spraying.

Some people maintain Kautsky came up with a socialist premature birth theory and believe it has been somewhat verified. Actually, the premature birth theory conceived by Kautsky referred to the pre...

The performance of cylinder liner-piston ring (CLPR) affects the efficiency of marine engine greatly. An experimental study on textured CLPR was conducted to seek insight into the operation reliability of CLPR. Three types of surface texture, groove texture on cylinder liner, dimple texture on piston ring, and co-texture on both sides, were processed. A series of tests were then carried out on an engine tester. Three characterization parameters, contact resistance, worn surface topography on cylinder liner, and cylinder pressure were used to describe the CLPR tribological properties and air tightness. The results showed that the three textures all improved tribological properties. Compared to the non-textured surface, the contact resistance of the three textures increased 30.7%, 71.7% and 98.4% on average. The wear resistance of dimple texture was weaker than that of groove texture. Air tightness was closely related to oil film pressure. At dead centre, the cylinder pressure of the three textures respectively was optimized by 4.6 kPa, 7.8 kPa and 12.3 kPa averagely. The co-texture was shown to combine the advantages of groove texture with the advantages of dimple texture, which provided the surface with improved oil film distribution and more efficient debris trapping, resulting in the optimum tribological properties and air tightness among the three textures.

Asymmetric casings filled with explosive have attracted increasing attention in the defence technology (e.g. innovative warhead design) and improvised explosive devices (IEDs) protection. As a typical asymmetric casing, D-shaped casing has been used in deformable aimable warhead, deployable aimable warhead as well as warhead in hypersonic weapons. To assist the design of asymmetric warhead, this work examined the velocity distribution of fragments from the bottom part of the D-shaped casing with different shell thickness. The fragment velocity distributions of the D-shaped casings with different shell thickness were numerically analyzed based on the SPH method. Numerical and theoretical analysis showed that there are opportunities to do optimization of shell thickness of D-shaped casings to maximum the utilization of the energy released by explosive. The findings herein could serve as a reference for further investigations on the fragment velocity distribution of D-shaped casings and provide a foundation for asymmetric warhead design.

In the field of defense technology and public security, asymmetric casings filled with explosive, especially the D-shaped casing, has received considerable attention. However, the effect of eccentric ratio on the fragment velocity distribution of D-shaped casing and its mechanism remain unclear. To obtain the velocity distribution of the fragments in the bottom part of the D-shaped casing, a kind of D-shaped casing with large length-diameter ratio was tested based on the X-ray photography technique. The experimental results show that the fragment velocity distribution of the D-shaped casing is not consistent with the results in existing studies. Then, a series of numerical simulation models were established and validated according to the experimental results, and the acceleration process of the fragments in the bottom part of D-shaped casing was numerically studied. The results indicate that the fragments in the bottom part of D-shaped casing are accelerated not only by the initial detonation wave but the detonation wave reflected from the arc part shell, which causes the inconsistency mentioned above. In addition, an empirical calculation formula was proposed based on the acceleration process of D-shaped casing and it was in a good accordance with numerical results. The findings herein could serve as a foundation for further research on the D-shaped casings and other kinds of asymmetric casings. It can also be a solid reference for engineering design of innovative warheads.

Aiming at the extraordinary dependency on manual experience during the process of sewage treatment, it is required to explore intelligent prediction mechanism for sewage quality. Due to the fact that convolutional neural network (CNN) has some unique advantages for fast prediction, this paper proposes a convolutional neural network-based prediction mechanism for sewage treatment (CPST). It contains two mains parts respectively named learning process and training process. A group of experiments are managed to evaluate the efficiency of the proposed CPST, and the results demonstrate that CPST obtain the lower prediction error compared with baselines.

Bi-layer structures with a water container and a fiber composite were designed for constructing explosion-proof equipment. The effects of the water position on the anti-fragment performance were explored by performing ballistic impact tests on bare water containers, bare fiber panels, water/fiber structures and fiber/water structures. For both UHMWPE and aramid fiber panels, the water/fiber structure exhibited a lager ballistic limit than the fiber/water structure, whose ballistic limit was even smaller than that of the corresponding bare fiber panel. Numerical models for the impacts of these targets with a UHMWPE panel were established and verified by the experimental results. The numerical results demonstrated that, for the UHMWPE/ water structure, the rear water weakened the ballistic performance of the UHMWPE panel mainly via enhancing the tensile stress in fiber direction, and thereby caused premature fiber fracture that was also observed in the experiments. For the water/UHMWPE structure, the ballistic performance of the rear UHMWPE panel was promoted compared with the bare UHMWPE panel at a high impact velocity, consistent with the experimental observation. It is because the water pre-accelerated the UHMWPE panel prior to projectile impact and thereby reduced the relative velocity between the projectile and the panel when it was penetrated.

The digital metering system has certain advantages in comparison with traditional metering systems in principle and performance, but the engineering application time is short. At present, there is a lack of research on the testability of digital metering systems. Reasonable determination of testability index allocation is an important issue to be addressed in the test requirements of digital systems. In this paper, the fuzzy comprehensive evaluation method is used to distribute the test index of smart substation system, which makes it more realistic. It can reflect the whole process of test distribution objectively and truly. Finally, combining with the communication network subsystem of substation, the proposed method is used to verify the testability distribution method, which shows that the method is feasible and effective.

With the installation and coverage rate of electricity information acquisition devices closing to 100%, the value of electricity information continuously highlight. Due to the sharply increase of electricity information data, the bottleneck of IO efficiency influences the further improvement of data processing efficiency. As “Read” plays a great role in IO, we focus on the promotion of the performance of “read”. As a result, we put forward a method with the fusion of LIFO and HRF (Highest Rank First), it not only takes into account the advantage of LIFO’s high hit rate of cache, but also solves the lower CPU utilization problem. The “read” performance has improved by 20% with the test on the data platform using our strategy, significantly improved the efficiency of IO.

Huang, T.; Guo, Z.; Wu, Z.; Zheng, Z., and Wang, C., 2019. Digital measurement method of power load change in port power supply. In: Guido-Aldana, P.A. and Mulahasan, S. (eds.), Advances i...

Amyand hernia is a rare form of inguinal hernia wherein the appendix is in the hernial sac. Moreover, the incidence of Amyand hernia is reportedly three times higher in children than in adults. Here, we report a case of Amyand hernia in the right groin of a 55-year-old patient admitted to our hospital. We describe our approach to the diagnosis and treatment of Amyand hernia in this case. Altogether, we conclude that reasonable individualized diagnosis and treatment for Amyand hernia according to the patient's conditions is warranted in such cases.

A \emph{linear $k$-forest} is a forest whose components are paths of length at most $k$. The \emph{linear $k$-arboricity} of a graph $G$, denoted by ${\rm la}_k(G)$, is the least number of linear $k$-forests needed to decompose $G$. Recently, Zuo, He and Xue studied the exact values of the linear $(n-1)$-arboricity of Cartesian products of various combinations of complete graphs, cycles, complete multipartite graphs. In this paper, for general $k$ we show that $\max\{{\rm la}_{k}(G),{\rm la}_{\ell}(H)\}\leq {\rm la}_{\max\{k,\ell\}}(G\Box H)\leq {\rm la}_{k}(G)+{\rm la}_{\ell}(H)$ for any two graphs $G$ and $H$. Denote by $G\circ H$, $G\times H$ and $G\boxtimes H$ the lexicographic product, direct product and strong product of two graphs $G$ and $H$, respectively. We also derive upper and lower bounds of ${\rm la}_{k}(G\circ H)$, ${\rm la}_{k}(G\times H)$ and ${\rm la}_{k}(G\boxtimes H)$ in this paper. The linear $k$-arboricity of a $2$-dimensional grid graph, a $r$-dimensional mesh, a $r$-dimensional torus, a $r$-dimensional generalized hypercube and a $2$-dimensional hyper Petersen network are also studied., Comment: 27 pages

Interval minors of bipartite graphs were introduced by Jacob Fox in the study of Stanley-Wilf limits. Recently, Mohar, Rafiey, Tayfeh-Rezaie and Wu investigated the maximum number of edges in $K_{k,\ell}$-interval minor free bipartite graphs when $k=2$ and $k=3$. In this paper, we investigate the maximum number of edges in $K_{k,\ell}$-interval minor free bipartite graphs for general $k$ and $\ell$. We also study the maximum number of edges in $K_{\ell_1,\ell_2,\cdots,\ell_t}$-interval minor free multipartite graphs., Comment: 9 pages. arXiv admin note: text overlap with arXiv:1408.1155 by other authors

The equitable coloring problem, introduced by Meyer in 1973, has received considerable attention and research. Recently, Wu, Zhang and Li introduced the concept of equitable $(t,k)$-tree-coloring, which can be regarded as a generalization of proper equitable $t$-coloring. The \emph{strong equitable vertex $k$-arboricity} of $G$, denoted by ${va_k}^\equiv(G)$, is the smallest integer $t$ such that $G$ has an equitable $(t', k)$-tree-coloring for every $t'\geq t$. The exact value of strong equitable vertex $k$-arboricity of complete equipartition bipartite graph $K_{n,n}$ was studied by Wu, Zhang and Li. In this paper, we first get a sharp upper bound of strong equitable vertex arboricity of complete bipartite graph$K_{n,n+\ell} \ (1\leq \ell\leq n)$, that is, ${va_2}^\equiv(K_{n,n+\ell})\leq2\left\lfloor{\frac{n+\ell+1}{3}}\right\rfloor$. Next, we obtain a sufficient and necessary condition on an equitable $(q,\infty)$-tree coloring of a complete equipartition tripartite graph, and study the strong equitable vertex arboricity of forests. For a simple graph $G$ of order $n$, we show that $1\leq {va_k}^\equiv(G)\leq \lceil n/2 \rceil$. Furthermore, graphs with ${va_k}^\equiv(G)=1,\lceil\frac{n}{2}\rceil,\lceil\frac{n}{2}\rceil-1$ are characterized, respectively. In the end, we obtain the Nordhaus-Gaddum type results of strong equitable vertex $k$-arboricity for general $k$., Comment: 14 pages, 0 figures

Physicochemical properties constitute a key factor for the success of a drug candidate. Whereas many strategies to improve the physicochemical properties of small heterocycle-type leads exist, complex hydrocarbon skeletons are more challenging to derivatize because of the absence of functional groups. A variety of C-H oxidation methods have been explored on the betulin skeleton to improve the solubility of this very bioactive, yet poorly water-soluble, natural product. Capitalizing on the innate reactivity of the molecule, as well as the few molecular handles present on the core, allowed oxidations at different positions across the pentacyclic structure. Enzymatic oxidations afforded several orthogonal oxidations to chemical methods. Solubility measurements showed an enhancement for many of the synthesized compounds.

Analytical target cascading (ATC) is a methodology for translating system design targets to design specifications for the elements comprising a decomposed engineering system. The paper introduces ATC to the application on the reliability allocation and presented a new algorithm based on exterior penalty function, called ATC-EPF. The method can deal with huge scale reliability allocation problem by the decomposition and coordination of targets between upper and lower level. The examples in the paper show that the proposed method can achieve good results as the same as the all-in-one method.

In this paper, a similar voice coil motor dual-axes precision platform is proposed. The voice coil motor consist with coil and permanent. Actuator theoremis due to the repelling force between the coil and the magnets affixed to the pad, and thrust is twice while making the platform operate, improve the shortcoming of voice coil motor with low thrust. Its stroke is 50 mm times 50 mm. First, the dynamic model is derived and analyzed. Next, an adaptive sliding mode controller is established. From simulation and experimental results, possible implementation, and satisfactory performance, and have been demonstrated.