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Generally, stochastic functional differential equations (SFDEs) pose a challenge as they often lack explicit exact solutions. Consequently, it becomes necessary to seek certain favorable conditions under which numerical solutions can converge towards the exact solutions. This article aims to delve into the convergence analysis of solutions for stochastic functional differential equations by employing the framework of G-Brownian motion. To establish the goal, we find a set of useful monotone type conditions and work within the space C r ((− ∞ , 0 ] ; R n) . The investigation conducted in this article confirms the mean square boundedness of solutions. Furthermore, this study enables us to compute both L G 2 and exponential estimates. [ABSTRACT FROM AUTHOR]

During the past two years, the novel coronavirus pandemic has dramatically affected the world by producing 4.8 million deaths. Mathematical modeling is one of the useful mathematical tools which has been used frequently to investigate the dynamics of various infectious diseases. It has been observed that the nature of the novel disease of coronavirus transmission differs everywhere, implying that it is not deterministic while having stochastic nature. In this paper, a stochastic mathematical model has been investigated to study the transmission dynamics of novel coronavirus disease under the effect of fluctuated disease propagation and vaccination because effective vaccination programs and interaction of humans play a significant role in every infectious disease prevention. We develop the epidemic problem by taking into account the extended version of the susceptible-infected-recovered model and with the aid of a stochastic differential equation. We then study the fundamental axioms for existence and uniqueness to show that the problem is mathematically and biologically feasible. The extinction of novel coronavirus and persistency are examined, and sufficient conditions resulted from our investigation. In the end, some graphical representations support the analytical findings and present the effect of vaccination and fluctuated environmental variation. [ABSTRACT FROM AUTHOR]

In this paper, the radial basis function (RBF) collocation method is applied to solve nonlinear partial differential equations (PDEs). First, the given equation is reduced to time-discrete form using Ө-weighted scheme. Then, with the help of RBFs, the given PDEs are transformed into a system of algebraic equations that is easy to solve. The proposed technique is verified by solving Hunter–Saxton and Gardner equations. For the solution of these problems, three types of RBFs, including multiquadric (MQ), inverse multiquadric (IMQ), and Gaussian (GA) have been used. The obtained solution is validated with the help of absolute error, L2, and L∞ error norms. The involved shape parameter is selected by the automatic algorithm that lies in the stable region of the method. The stability of the scheme is discussed by the spectral matrix method and validated computationally. [ABSTRACT FROM AUTHOR]

Background: Ω-3 fatty acids perform several therapeutic functions in the body, however, their applications are limited due to the inferior oxidative stability. To improve the oxidative stability and release properties of Ω-3 fatty acids, microencapsulation is performed. Butter is a good source of fat-soluble vitamins and antioxidant systems however, it is not a good source of Ω-3 fatty acids. Supplementation of butter with microcapsules of vegetable oils rich in Ω-3 fatty acids is not reported in literature. Methods: Microcapsules of chia oil (MCO) were prepared using chitosan as encapsulating material by spray drying at lower temperature. Unsalted butter prepared from cultured cream using Lactococcus lactis ssp. Lactis at 21 °C for 16 Hrs. Cream was churned at 12 °C and microcapsules of chia oil were added to the butter during the working stage at four different concentrations i.e. 2, 4, 6 and 8% (T1, T2, T3 and T4, respectively). Butter without supplementation of MCO were kept as control. Butter samples were stored for 90 days at -10 °C. Butter composition, antioxidant capacity, fatty acid profile, induction period, free fatty acids, peroxide value and sensory evaluation were performed at 0, 45 and 90 days of storage. Results: Addition of MCO in butter did not have any effect on standards of identity of butter. Microencapsulation had no effect on fatty acid profile of microcapsules of chia oil. Concentration of alpha-linolenic acid (ALA) in control, T1, T2, T3 and T4 were 0.49, 4.29, 8.41, 13.21 and 17.44%, respectively. Concentration of ALA in fresh and 90 days stored butter samples were 17.44 and 17.11%, respectively. After 90 days of storage, loss of eicosapentaenoic acid (EPA), docosapentaenoic acid (DPA) and docosahexaenoic acid (DHA) were 0.07%, 0.05 and 0.03%, respectively. At 0, 45 and 90 days of storage, 2, 2-Diphenyl-1-picrylhydrazyle (DPPH) free radical scavenging activity of free chia oil was 39.81, 71.22 and 62.18%, respectively. However, microcapsules of chia oil had superior antioxidant activity. DPPH free radical scavenging activity of microcapsules at 0, 45 and 90 days of storage was 36.51, 36.43 and 35.96%, respectively (p > 0.05). Total antioxidant capacity of microcapsules at 0, 45 and 90 days of storage was 70.53, 69.88 and 68.52%, respectively (p > 0.05). It was recorded that induction period of free chia oil and microcapsules was only 2.86 h and 8.55 h. Among the butter samples, control revealed the lowest induction period. While, induction period of experimental samples was not different from each other. Peroxide value and free fatty acids of the butter samples at the end of storage period (90 days) was less than the European Union standards limit (10MeqO2/kg and 0.2%). Sensory characteristics of experimental samples were similar to the control. MCO can be added in butter to improve its functional value. Conclusion: Concentration of Ω-3 fatty acids in butter up to 8% can be increased through microcapsules of chia oil with reasonable oxidative stability and no effect on sensory characteristics. [ABSTRACT FROM AUTHOR]

This research concentrates on the analysis of meromorphic mappings. We derived several important results for value distribution of specific difference polynomials of meromorphic mappings, which generalize the work of Laine and Yang. In addition, we proved uniqueness theorems of meromorphic mappings. The difference polynomials of these functions have the same fixed points or share a nonzero value. This extends the research work of Qi, Yang and Liu, where they used the finite ordered meromorphic mappings. [ABSTRACT FROM AUTHOR]

Background: Chia (Salvia hispanica L.) has been regarded as good source of polyunsaturated omega-3 fatty acids with cardiac, hepatic, hypotensive, antiallergic and antidiabetic role. Concentration of omega-3 fatty acids in chia oil can be enhanced by fractionation. Olein/low melting fraction of chia oil has higher concentration of omega-3 fatty acids. Therefore, main objective of current investigation was determination of various concentration effect of olein fraction of chia oil on omega-3 fatty acids, oxidative stability and sensory characteristics of ice cream. Methods: Ice cream samples were prepared by partially replacing the milk fat with olein fraction of chia oil at 5, 10, 15 and 20% concentrations (T1, T2, T3 and T4), respectively. Ice cream prepared from 100% milk fat was kept as control. Ice cream samples stored at -18 °C for 60 days were analysed at 0, 30 and 60 days of the storage period. Fatty acid profile, total phenolic contents, total flavonoids, free fatty acids, peroxide value, anisidine value and sensory characteristics of ice cream samples was studied. Results: Concentration of α-linolenic acid, eicosapentaenoic acid, docosapentaenoic acid and docosahexaenoic acid in T4 was 13.24, 0.58, 0.42 and 0.31%, respectively. Total phenolic contents of control, T1, T2, T3 and T4 were recorded 0.12, 1.65, 3.17, 5.19 and 7.48 mg GAE/mL, respectively. Total flavonoid content of control, T1, T2, T3 and T4 were found 0.08, 0. 64, 1.87, 3.16 and 4.29 mg Quercetin Equivalent/mL. 2,2-diphenyl-1-picrylhydrazyl (DPPH) free radical scavenging activity of control, T1, T2, T3 and T4 was noted 5.61, 17.43, 36.84, 51.17 and 74.91%, respectively. After 60 days of storage period, the highest peroxide value of 1.84 (MeqO2/kg) was observed in T4, which was much less than allowable limit of 10 (MeqO2/kg). Flavour score was non-significant after 30 days of storage period. Conclusions: Supplementation of ice cream with olein fraction of chia oil enhanced the concentration of omega-3 fatty acids and improved the antioxidant perspectives of ice cream. These results suggest that omega-3 fatty acids and antioxidant characteristics of ice cream may be improved with olein fraction of chia oil for discerning consumers. [ABSTRACT FROM AUTHOR]

Oleic acid in butter oil (BO) was enhanced by a high oleic acid fraction (HOF) of Moringa oleifera oil (MOO). HOF was blended with BO at four different concentrations i.e. 5%, 10%, 15% and 20% (HOF-5, HOF-10, HOF-15 and HOF-20, respectively), compared with a control (BO). The oleic acid in HOF increased from 71.55% to 80.25%. DPPH free radical scavenging activity and total flavonoid content of HOF was 76.88% and 34.52 mg/100 g. Supplemenation of butter oil with 20% HOF, decreased the cholesterol from 224 to 177 mg/100 g. Peroxide value of three months stored HOF-20 was 1.18 (meqO2/ kg) as compared to control, 3.15 (meqO2/kg). Induction period of HOF-20 was 4.07 h greater than control. These results evidenced that oleic acid in butter oil can be substantially increased by HOF of MOO. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the effect of high melting point interesterified M. oleifera oil (35.6°C) with substantial amount of unsaturated fatty acids on physicochemical and oxidative stability characteristics of ice cream. Of the 10% fat in the ice cream, 30% was replaced by interesterified M. oleifera oil at three levels i.e. 10, 20 and 30% (T1, T2 and T3, respectively). Oleic acid increased from 26.55% to 31.69%, 36.94% and 42.15% in T1, T2 and T3 with no effect on melting time, compositional attributes and free fatty acid content of ice cream (P>0.05). Supplementation of ice cream with interesterified M. oleifera oil inhibited the autoxidation process in ice cream during 3 months storage period (P<0.05).The loss of oleic and linoleic acid in fresh and 3 months stored control and T2 was 26.55%, 24.15%, 26.39% and 1.93%, 1.24% and 1.79%, respectively. Peroxide value of three months stored control and T3 was 1.12 and 0.39 (meqO2/kg). The overall acceptability score of T2 was 80% of the total score (9). [ABSTRACT FROM AUTHOR]

We develop a model and investigate the temporal dynamics of the transmission of the novel coronavirus. The main sources of the coronavirus disease were bats and unknown hosts, which left the infection in the seafood market and became the major cause of the spread among the population. Evidence shows that the infection spiked due to the interaction between humans. Hence, the formulation of the model proposed in this study is based on human-to-human and reservoir-to-human interaction. We formulate the model by keeping in view the esthetic of the novel disease. We then fractionalize it with the application of fractional calculus. Particularly, we will use the Caputo–Fabrizio operator for fractionalization. We analyze the existence and uniqueness of the well-known fixed point theory. Moreover, it will be proven that the considered model is biologically and mathematically feasible. We also calculate the threshold quantity (reproductive number) to discuss steady states and to show that the particular epidemic model is stable asymptotically under some restrictions. We also discuss the sensitivity analysis of the threshold quantity to find the relative impact of every epidemic parameter on the transmission of the coronavirus disease. Both the global and local properties of the proposed model will be analyzed for the developed model using the mean value theorem, Barbalat's lemma, and linearization. We also performed some numerical simulations to verify the theoretical work via some graphical representations. [ABSTRACT FROM AUTHOR]

The present study investigated the effect of leadership styles on knowledge management. The population of the study consists of faculty and administrative staff of public sector universities of Khyber Pakhtunkhwa. To test the study hypotheses, correlation and regression analysis were conducted. The study found that transformational leadership style has positive and significant relation with knowledge management effectiveness. The study found that transactional leadership style has negative but significant relationship with knowledge management effectiveness. The study concluded that educational institutions should adopt transformational leadership style in order to improve knowledge management effectiveness. Educational leaders should not adopt transactional leadership style as that type of leadership negatively affects knowledge management. The study recommended that leaders of the educational institutions should get involved their subordinates in decision making process in order to further enhance their performance. Managerial implications, recommendations and directions for future research are also highlighted. [ABSTRACT FROM AUTHOR]

The current rate of population growth is so fast that, to feed this massive population, a 2-fold increase in land is required for the production of quality food. Improved dietary products such as milk and its products with antioxidant properties and functional foods of animal origin have been utilized to prevent chronic diseases. The designer milk contains low fat and less lactose, more protein, modified level of fatty acids, and desired amino acid profiles. The importance of milk and its products is due to the presence of protein, bioactive peptides, conjugated linoleic acid, omega-3 fatty acid, Vitamin D, selenium, and calcium. These constituents are present in milk product, play a key role in the physiological activities in human bodies, and act as anti-inflammatory, anti-tumor, antioxidant, hypocholesterolemic, immune boosting, and antimicrobial activities. Consumer awareness regarding benefits of designer foods such as milk and its products is almost non-existent worldwide and needs to be established to reach the benefits of designer food technologies in the near future. The main objective of this review was to collect data on the antioxidant properties of milk and its constituents which keep milk-derived products safe and preserved. [ABSTRACT FROM AUTHOR]

In this article, we focus on the numerical study of one and two dimensional higher order multi-term time fractional partial differential equations. In the adopted strategy, the temporal fractional derivative is replaced via well known L 1 formula and the integer order space derivatives are approximated by truncated one and two dimensional wavelet series. The fascinating nature of the scheme is to use collocation approach which convert the governing equations to the system of algebraic equations from which the wavelet coefficients can be calculated. Next, stability of the proposed scheme is investigated theoretically which is also the fundamental subject of the current work. Further computational convergence rate is computed which predicts that the order is approximately two. The scheme is applied to solve one dimensional beam models (fourth order partial differential equations) and two dimensional fissured rock models (Sobolev equations). Efficiency of the scheme is examined with the help of various error norms such as I ∞ , I r m s and I 2. Simulations indicate pretty much good results from which we can say that the scheme is suitable and robust for both one and two dimensional problems. [ABSTRACT FROM AUTHOR]

In this article, we extend the notion of double Laplace transformation to triple and fourth order. We first develop theory for the extended Laplace transformations and then exploit it for analytical solution of fractional order partial differential equations (FOPDEs) in three dimensions. The fractional derivatives have been taken in the Caputo sense. As a particular example, we consider a fractional order three dimensional homogeneous heat equation and apply the extended notion for its analytical solution. We then perform numerical simulations to support and verify our analytical calculations. We use Fox-function theory to present the derived solution in compact form. [ABSTRACT FROM AUTHOR]

In the present study photo-oxidative stability of pasteurized milk packaged in polyethylene pouches was investigated. Milk packaged in three layer polyethylene pouch packs was exposed to 400, 600 and 800 l×florescent light at 4 °C for 6 days, compared with a control (stored in dark). Light had a pronounced effect on fat content of milk with no effect on protein, lactose and ash content. Photo-oxidative stability of milk decreased as the intensity of light increased, peroxide value, anisidine value and conjugated dienes increased during the storage period of 6 days, higher values were observed in samples exposed to 800 l×florescent light. After 6 days of storage period, milk exposed to 400 l×florescent light did not reveal any oxidized flavour. The results of this study depicted that polyethylene pouches have the capability to resist photo-oxidation up to 400 l×ight. [ABSTRACT FROM AUTHOR]

In the present study photo-oxidative stability of pasteurized milk packaged in polyethylene pouches was investigated. Milk packaged in three layer polyethylene pouch packs was exposed to 400, 600 and 800 l× florescent light at 4 °C for 6 days, compared with a control (stored in dark). Light had a pronounced effect on fat content of milk with no effect on protein, lactose and ash content. Photo-oxidative stability of milk decreased as the intensity of light increased, peroxide value, anisidine value and conjugated dienes increased during the storage period of 6 days, higher values were observed in samples exposed to 800 l× florescent light. After 6 days of storage period, milk exposed to 400 l× florescent light did not reveal any oxidized flavour. The results of this study depicted that polyethylene pouches have the capability to resist photo-oxidation up to 400 l× light. [ABSTRACT FROM AUTHOR]

The present study focuses on fabrication of magnetic activated carbon (M-AC) using tire waste and its potential investigation for adsorption of Cr (VI) from wastewater. The composite material (M-AC) was synthesized by pyrolysis followed by in situ magnetization method, and characterized by FTIR, FESEM, EDX, and XRD analysis. The maximum adsorption of Cr (VI) ion over composite adsorbent was found (~99.5%) to occur at pH 2, sample volume 10 mL, adsorbent dose 100 mg, contact time 30 min. The adsorption process was endothermic, feasible, spontaneous, and was found to follow pseudo second order of the reaction. The Cr ion could be completely desorbed (~99.3%) from the composite adsorbent by using 20 mL of 2 M NaOH solution. The composite adsorbent was regenerated by continuous adsorption and desorption for 5 consecutive cycles by using 10 mL 0.1 M HCl solution. M-AC also performed well in case of tannery wastewater by removing about 97% of Cr (VI). [ABSTRACT FROM AUTHOR]

Milk and dairy products are integral part of human nutrition and they are considered as the carriers of higher biological value proteins, calcium, essential fatty acids, amino acids, fat, water soluble vitamins and several bioactive compounds that are highly significant for several biochemical and physiological functions. In recent years, foods containing natural antioxidants are becoming popular all over the world as antioxidants can neutralize and scavenge the free radicals and their harmful effects, which are continuously produced in the biological body. Uncontrolled free radicals activity can lead to oxidative stresses, which have been implicated in breakdown of vital biochemical compounds such as lipids, protein, DNA which may lead to diabetes, accelerated ageing, carcinogenesis and cardiovascular diseases. Antioxidant capacity of milk and milk products is mainly due to sulfur containing amino acids, such as cysteine, phosphate, vitamins A, E, carotenoids, zinc, selenium, enzyme systems, superoxide dismutase, catalase, glutathione peroxidase, milk oligosaccharides and peptides that are produced during fermentation and cheese ripening. Antioxidant activity of milk and dairy products can be enhanced by phytochemicals supplementation while fermented dairy products have been reported contained higher antioxidant capacity as compared to the non-fermented dairy products. Literature review has shown that milk and dairy products have antioxidant capacity, however, information regarding the antioxidant capacity of milk and dairy products has not been previously compiled. This review briefly describes the nutritional and antioxidant capacity of milk and dairy products. [ABSTRACT FROM AUTHOR]

We conducted petrographic, geochemical, and new U–Pb laser ablation inductively coupled mass spectrometry analyses of detrital zircons in the sandstone samples from the important Mengqiguer sandstone-type uranium deposit located in the Yili basin of the Xishanyao Formation. This formation (Shuixigou Group) is a major uranium-bearing target stratum in the basin. The main purpose of our investigations was to determine the provenance of the host sand units that has remained unclear to date. Our petrographic results suggested that the host sandstone is texturally and chemically immature, indicating superior physicochemical conditions for later uranium mineralisation. The major and trace element data of the detrital sandstone samples point towards the upper continental crust, and the chondrite-normalised rare earth element (REE) plots show enriched light REE and relatively flat heavy-REE distribution, with a negative Eu anomaly. The characteristics of the REEs and the trace elements point to felsic rocks as the provenance of the target strata with a continental arc tectonic setting. The detrital zircons indicate an age span of ∼235–∼2327 Ma, with major age populations of ∼300–∼500 Ma. The increasing amount of zircon grains from the Late Devonian to the Early Carboniferous coinciding with the age of volcanic magmatic activities of the Wusun and Nalati mountains indicates that the rocks formed under the Tianshan collisional orogeny and the subsequent extensional environment. [ABSTRACT FROM AUTHOR]

Background: Among the dietary lipids, milk fat is most complicated as it contains more than one hundred types of fatty acids and several triglycerides. Huge versatility in triglyceride and fatty composition makes it possible to convert milk fat into various fractions on the basis of melting characteristics. Functional properties of milk fat can be increased by converting it into different fractions. After cow milk, buffalo milk is the second largest source of milk and chemical characteristics of buffalo milk fat has been studied in a limited fashion. The main mandate was determination of triglyceride, fatty acid profile and antioxidant characteristics of low melting point fractions of buffalo milk fat for increased industrial applications. Methods: Buffalo milk fat (cream) was fractionated at three different temperatures i.e. 25, 15 and 10 °C by dry fractionation technique and packaged in 250 ml amber glass bottles and stored at ambient temperature for 90 days. The fraction of milk fat harvested at 25, 15 and 10 °C were declared as LMPF-25, LMPF-15 and LMPF-10. Unmodified milk fat was used as control (PBMF). Low melting point fractions were analyzed for triglyceride composition, fatty acid profile, total phenolic contents, DPPH free radicals scavenging activity, reducing power, free fatty acids, peroxide value, iodine value and conjugated dienes at 0, 45 and 90 days of storage. Results: In LMPF-10, concentrations of C36, C38, C40, and C42 were 2.58, 3.68, 6.49 and 3.85% lower than PBMF. In LMPF-25, concentrations of C44, C46, C48, C50, C52 and C54 were 0.71, 1.15, 2.53, 4.8, 0.39 and 2.39% higher than PBMF. In LMPF-15, concentrations of C44, C46, C48, C50, C52 and C54 were 2.45, 4.2, 3.47, 5.92, 2.38 and 3.16% higher than PBMF. In LMPF-10, concentrations of C44, C46, C48, C50, C52 and C54 were 2.8, 5.6, 5.37, 7.81, 3.81 and 4.45% higher than PBMF. LMPF-25, LMPF-15 and LMPF-10 had higher concentration of unsaturated fatty acids as compared PBMF. Total phenolic contents of buffalo milk fat and its fractions were in the order of LMPF-10 > LMPF-15, LMPF-25 > PBMF. Storage period of 45 days had a non-significant effect on total flavonoid content. 2, 2-Diphenyl-1-picrylhydrazyl free radical scavenging activity (DPPH) free radical scavenging activity of LMP-25, LMPF-15 and LMPF-10 were 4.8, 13.11 and 25.79% higher than PBMF. Reducing power of PBMF, LMPF-25, LMPF-15 and LMPF-10 were 22.81, 28.47, 37.51 and 48.14, respectively. Estimation of free fatty acids after the 90 days of storage duration, no significant difference was found in content of free fatty acids in unmodified milk fat and low melting point fractions. Testing of peroxide value in 90 days old samples showed that peroxide value of PBMF, LMPF-25, LMPF-15 and LMPF-10 was 0.54, 0.98, 1.46 and 2.22 (MeqO2/kg), respectively. Storage period up to 45 days had a non-significant effect on anisidine value, iodine value and conjugated dienes. Conclusion: Low melting point fractions of buffalo milk fat had higher concentration of unsaturated fatty acids and more antioxidant capacity than unmodified milk fat with reasonable storage stability. [ABSTRACT FROM AUTHOR]