Signorini-Type Problems over Non-Convex Sets for Composite Bodies Contacting by Sharp Edges of Rigid Inclusions

A new type of non-classical 2D contact problem formulated over non-convex admissible sets is proposed. Specifically, we suppose that a composite body in its undeformed state touches a wedge-shaped rigid obstacle at a single contact point. Composite bodies under investigation consist of an elastic matrix and a rigid inclusion. In this case, the displacements on the set, corresponding to a rigid inclusion, have a predetermined structure that describes possible parallel shifts and rotations of the inclusion. The rigid inclusion is located on the external boundary and has the form of a wedge. The presence of the rigid inclusion imposes a new type of non-penetration condition for certain geometrical configurations of the obstacle and the body near the contact point. The sharp-shaped edges of the obstacle effect such sets of admissible displacements that may be non-convex. For the case of a thin rigid inclusion, which is described by a curve and a volume (bulk) rigid inclusion specified in a subdomain, the energy minimization problems are formulated. The solvability of the corresponding boundary value problems is proved, based on analysis of auxiliary minimization problems formulated over convex sets. Qualitative properties of the auxiliary variational problems are revealed; in particular, we have found their equivalent differential formulations. As the most important result of this study, we provide justification for a new type of mathematical model for 2D contact problems for reinforced composite bodies.

A nonlinear population dynamics model of patient diagnosis and treatment involving in two level medical institutions and its qualitative analysis of positive singularity

<abstract><p>In this article, we firstly establish a nonlinear population dynamical model to describe the changes and interaction of the density of patient population of China's primary medical institutions (PHCIs) and hospitals in China's medical system. Next we get some sufficient conditions of existence of positive singularity by utilising homotopy invariance theorem of topological degree. Meanwhile, we study the qualitative properties of positive singularity based on Perron's first theorem. Furthermore, we briefly analyze the significance and function of the mathematical results obtained in this paper in practical application. As verifications, some numerical examples are ultimately exploited the correctness of our main results. Combined with the numerical simulation results and practical application, we give some corresponding suggestions. Our research can provide a certain theoretical basis for government departments to formulate relevant policies.</p></abstract>

Some qualitative properties of nonlinear fractional integro-differential equations of variable order

The existence-uniqueness criteria of nonlinear fractional integro-differential equations of variable order with multiterm boundary value conditions are considered in this work. By utilizing the concepts of generalized intervals combined with the piecewise constant functions, we transform our problem into usual Caputo’s fractional differential equations of constant order. We develop the necessary criteria for assuring the solution's existence and uniqueness by applying Schauder and Banach fixed point theorem. We also examine the stability of the derived solution in the Ulam-Hyers-Rassias (UHR) sense and provide an example to demonstrate the credibility of the results.

Development of flour confectionery products with reduced sugar content

The search for equivalent flavoring sugar substitutes of a non-sugar nature is an urgent direction in the development of the technology of flour confectionery products. In the course of research, a gingerbread recipe has been developed with a partial replacement of the prescription sugar with a 15 % solution of sucralose in glycerin, which most closely correspond to the organoleptic characteristics (taste, smell, texture) of traditional flour confectionery products. The results of the organoleptic evaluation of coded prototypes of gingerbread with the involvement of experts have shown that a decrease in sugar concentration by 25 % does not lead to a statistically significant change in organoleptic parameters in comparison with control samples. Substitution of more than 30 % sugar leads to an increase in the plasticity of the dough complicating the operation of the dosing mechanisms; at the same time, the taste of the products changes (these changes are noted during the tasting assessment); their consistency becomes denser. In the process of research, the stability of the quantitative and qualitative properties of gingerbread during storage has been proved. Experimental samples of gingerbread with 25 % reduced sugar content retain all the indicators established by GOST for their storage for 90 days without statistically significant changes. The decomposition of sucralose in the manufacture of the dough is 0.1 %, in the baking process - 2.6 %, during storage for 120 days - 6.7 % (of the loaded product). The developed recipe allows enterprises to expand the range of confectionery products with reduced sugar content.

Interactive Effects of Nitrogen and Potassium Fertilizers on Quantitative-Qualitative Traits and Drought Tolerance Indices of Rainfed Wheat Cultivar

Increasing global food requirements and global warming are two challenges of future food security. Water availability and nutrient management are two important factors that affect high-yield and high-quality wheat production. The main and interactive effects of nitrogen and potassium fertilizers on quantitative-qualitative properties and drought tolerance of an Iranian rainfed cultivar of wheat, Azar-2, were evaluated. Four rates of nitrogen (N0, N30, N60, and N90 kg/ha), along with four concentrations of potassium (K0, K30, K60, and K90 kg/ha), were applied in rainfed (drought stress) and non-stress conditions. The interactive effect of N × K was significant on nitrogen and protein contents of grains at 5% and 1% probability levels, respectively. Different trends of SSI, STI, K1STI, and K2STI indexes were observed with the interactive levels of nitrogen and potassium. The lowest SSI index (0.67) was observed in N30K30, whereas the highest STI (1.07), K1STI (1.46), and K2STI (1.51) indexes were obtained by N90K60 and N90K90. The obtained results could be useful to increase yield and quality of winter rainfed wheat cultivars under drought stress with cool-rainfed areas. N60K30 and N90K60 can be recommended to increase the grain yield and protein content of rainfed wheat under drought stress and non-stress conditions, respectively.

Improvement in the Quality Attributes of Forage Cowpea by Use of Liquid Microbial Inoculants

Background: The present investigation was accepted to study the impact of liquid microbial inoculants on the quality parameters of forage cowpea (Vigna unguiculata). There upon, the field experiment was conducted during kharif 2018 at Punjab Agricultural University, Regional Research Station, Bathinda and at Department of Plant Breeding and Genetics, Punjab Agricultural University, Ludhiana, Punjab respectively. Methods: The experiment was laid out in randomized complete block design with a total of eleven treatment combinations of liquid microbial inoculants (Burkholderia seminalis, Burkholderia sp. and Bradyrhizobium sp.) with 75% and 100% RDF and replicated thrice. The qualitative properties including crude protein (CP), neutral detergent fibre (NDF), acid detergent fibre (ADF), in-vitro dry matter digestibility (IVDMD), total soluble sugars and ash content were determined on the forage samples. Result: The results indicated that the treatment T10 (75% RDF + Burkholderia sp. + Burkholderia seminalis) has reduced ADF% and NDF% at both the locations. Forage with high ADF and NDF% content tends to have low digestibility, low ADF and NDF% is desirable. In addition, treatment T10 showed significantly (p less than 0.05) improved IVDMD (79.98%) and total sugars (15.82 mg/g) at Ludhiana and at Bathinda, T10 treatment significantly escalated crude protein (19.93%), total ash content (11.55%), total chlorophyll content (2.07 mg/g) and total sugars (15.80 mg/g).Further correlation studies showed highly significant positive correlation among ADF% and NDF% and there negative correlation with all other quality components at both the locations. Consequently, liquid microbial inoculants can play pertinent role in ameliorating fibre quality and interrelation between the various quality parameters proposed that forage with low ADF% and NDF% can be selected for simultaneous amelioration in different attributes of quality.

Modeling the Process of School Shooters Radicalization (Russian Case)

Research on radicalization became relevant to the study of terrorism and violent extremism just two decades ago. The accumulated empirical data on terrorism have led researchers and experts to understand that radicalization is a predictor of violent actions by terrorists, violent extremists, and lone actors. Violent incidents committed by school shooters are not terrorist crimes, but there is good reasons for inclusion as terrorist crimes since they have similar mechanisms. The article aims to create a conceptual model of school-shooter radicalization and determine the distinguishing features of the process. The paper presents a theoretical and methodological base of content analysis concepts, political models, and terrorist radicalization on the different levels of study. Based on the content analysis results, we identify the significant gaps in the research field, consider the radicalization phenomenon in detail, substantiated the qualitative aspects of the school shooters radicalization, and propose a conceptual scheme. Psychological, behavioral, cognitive aspects of the school shooters radicalization reflect a holistic picture of the relationship between the process phases and changes in the parameters of the object’s state. The aspects of radicalization and this phenomenon’s qualitative properties are interpreted as the determinants of the conceptual model. The model includes five stages, each of which is considered to be one of the components for the formation and acceptance of the idea of a violent way to solve a problem, but certainly do not act individually as the only component that leads to the actual implementation of the incident of a school shooting. An in-depth study of online social connections and warning signs, mobilization factors, behavioral trajectories, and imitation mechanisms can help scientists understand why school shooters are increasingly motivated to use violent means to achieve personal goals. We have outlined the possibilities and prospects of the model’s application and directions for future research.

Nodal Multi-peak Standing Waves of Fourth-Order Schrödinger Equations with Mixed Dispersion

We consider the existence and concentration properties of standing waves for a fourth-order Schrödinger equation with mixed dispersion, which was introduced to regularize and stabilize solutions to the classical time-dependent Schrödinger equation. This leads to study multi-peak solutions to the following singularly perturbed fourth-order nonlinear Schrödinger equation $$\begin{aligned} {\varepsilon ^{\text {4}}}{\Delta ^{\text {2}}}u - \beta {\varepsilon ^2}\Delta u + V(x)u = |u{|^{p - 2}}u{\text { in }}{\mathbb {R}^N},{\text { }}u \in {H^2}({\mathbb {R}^N}). \end{aligned}$$ ε 4 Δ 2 u - β ε 2 Δ u + V ( x ) u = | u | p - 2 u in R N , u ∈ H 2 ( R N ) . We first establish a local $${W^{4,p}}$$ W 4 , p -estimate for a class of fourth-order semilinear elliptic equations, which is a key to get the uniform and global $${L^\infty }$$ L ∞ -estimate of solutions to the considered singularly perturbed equation above. Next, under certain assumptions on $$\beta $$ β and the potential V(x), we construct a family of sign-changing multi-peak solutions with a unique maximum (or minimum) point on each component. We prove that these solutions concentrate around any prescribed finite set of local minima (possibly degenerate) of the potential V(x). Compared with the classical singularly perturbed Schrödinger equation, the presence of a fourth-order term in the problem above forces the development of new techniques to obtain qualitative properties of multi-peak solutions.