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In this paper, we study the existence of multiple solutions for the following biharmonic problem Δ 2 u = f (x , u) + g (x , u) in Ω , u = Δ u = 0 on ∂ Ω , where Ω ⊂ R N , (N > 4) is a smooth bounded domain and f (x , ξ) is odd in ξ , g (x , ξ) is a perturbation term. By using the variant of Rabinowitz's perturbation method, under some growth conditions on f and g, we show that there are infinitely many weak solutions to the problem. [ABSTRACT FROM AUTHOR]

Copyright of Estudios Demográficos y Urbanos is the property of El Colegio de Mexico AC and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let Ω ⊂ C be a bounded domain. In this note, we use complex variable methods to study the number of critical points of the function v = v Ω that solves the elliptic problem Δ v = - 2 in Ω , with boundary values v = 0 on ∂ Ω. This problem has a classical flavor but is especially motivated by recent studies on localization of eigenfunctions. We provide an upper bound on the number of critical points of v when Ω belongs to a special class of domains in the plane, namely, domains for which the boundary ∂ Ω is contained in { z : | z | 2 = f (z) + f (z) ¯ } , where f ′ (z) is a rational function. We furnish examples of domains where this bound is attained. We also prove a bound on the number of critical points in the case when Ω is a quadrature domain. The note concludes with the statement of some open problems and conjectures. [ABSTRACT FROM AUTHOR]

Technological expertise of food production is an extremely important competence for the production process. Technological expertise of food production has many points of contact with quality and safety management systems. In order to regulate the quality and safety of food products at the legislation level, it is indispensable for companies to implement quality and safety management systems that are harmonized with international standards. To implement the legal requirements, manufacturers must adhere to good hygiene and good manufacturing practices for the implementation of prerequisites for production, as well as the principles of the HACCP system. in practice, manufacturers are faced many problems that require a deep understanding, a scientific approach. One of the steps in the implementation of the HACCP system is a detailed description of the technological scheme of production and modes of technological processes. Validation of control measures is used to establish the correct technological regimes, because otherwise a hazard may arise, which will further affect the quality and safety of products. The paper provides recommendations for the selection of methods for validation of control measures of significant hazards in the production of milk and canned (fruits and vegetables) products as a necessary element of technological expertise and quality and safety management systems. It was provide a brief description of the such food groups as milk products and canned products (fruit and vegetable) from the technological expertise view of point. For both of these groups hazards have been identified in the technologies and significant hazards were detected. The validation methods of significant hazards control measures in the production of a specific group of food products were analyzed, that can improve deeper understanding of processes and, therefore, risk reduction in problem prevention and process management. [ABSTRACT FROM AUTHOR]

Various applications in science and engineering depend upon computing real solutions to systems of analytic equations which depend upon real parameters. Locally in the parameter space, the qualitative behavior of the solutions remains the same except at critical parameter values. This article develops a singular value homotopy that aims to compute critical parameter values. Several examples are presented including computing critical parameter values for nonlinear boundary value problems, turning points for a steady-state system connected to learning and memory, and computing the maximum Gaussian curvature of a surface. [ABSTRACT FROM AUTHOR]

The present study deals with a computational investigation on the role of dithiocarbamate (DTC) anions in the stabilization of σ-aromatic trinuclear mono-cationic metal clusters (M = Cu, Ag and Au). Electrostatic potential, aromaticity, binding energy, thermodynamical parameters and nature of bonding are estimated. Nucleus independent chemical shifts (NICS) and their variants such as NICStotal and FiPC-NICS are employed to calculate aromaticity. The nature of bonding is assessed by the quantum theory of atoms-in-molecules (QT-AIM) and NBO methods. The charge density map in the complex has been assessed by molecular electrostatic potential analysis. Comparison of complexation properties of DTC ligand to common monodentate ligands (pyrazolates, NHC, pyridine, furan and isoxazole) explored in past reveal that DTC anions are more efficient in stabilizing metal complexes. Synopsis. A computational approach is undertaken to investigate complexation properties of dithiocarbamate (DTC) anions with electron-deficient M3+ (M = Cu, Ag & Au) clusters. DTC ligands are found to be efficient chelators as compared to commonly used monodentate ligands to bind and stabilize such unstable trinuclear mono-cationic metal clusters [ABSTRACT FROM AUTHOR]

We study the Wasserstein metric W p , a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance W 1 between the distribution of quadratic residues in a finite field F p and uniform distribution by ≲ p - 1 / 2 (the Polya–Vinogradov inequality implies ≲ p - 1 / 2 log p ). We also show that for continuous f : T → R with mean value 0 (number of roots of f) · ∑ k = 1 ∞ | f ^ (k) | 2 k 2 1 2 ≳ ‖ f ‖ L 1 (T) 2 ‖ f ‖ L ∞ (T) . Moreover, we show that for a Laplacian eigenfunction - Δ g ϕ λ = λ ϕ λ on a compact Riemannian manifold W p max ϕ λ , 0 d x , max - ϕ λ , 0 d x ≲ p log λ / λ ‖ ϕ λ ‖ L 1 1 / p , which is at most a factor log λ away from sharp. Several other problems are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we study the supercritical problem (P ε) : - ▵ u = K | u | 4 / (n - 2) + ε u in Ω , u = 0 on ∂ Ω , where Ω is a smooth bounded domain in R n , n = 3 , 4 , ε is a positive real parameter and K is a C 4 positive function on Ω ¯ . Following the ideas of Bahri et al. (Calc Var Partial Differ Equ 8:67–93, 1995) and using the finite-dimensional reduction, we construct some solutions of (P ε) . [ABSTRACT FROM AUTHOR]

Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption. [ABSTRACT FROM AUTHOR]

Nowadays, the topology of electron density (ED) distributions as well as the non-covalent interaction (NCI) analysis of reduced density gradient (RDG) distributions, are extensively used to characterize intermolecular contacts. Here, topological and NCI-based analyses are combined for the multiresolution study of the intermolecular interactions occurring in a drug-protein system (PDB access code: 3UNK). The method involves the search for the critical points (CP) of the well-known PASA model developed by Carbó-Dorca and co-workers, and the minima in the corresponding RDG grids. The CP-based representation of the intermolecular contacts enriches the geometry-based interactions found using a Web server. The stability of the intermolecular interactions is studied by following their corresponding CP trajectory in space at several degrees of the ED smoothing, and by the evaluation of the local potential energy density (LPDE). It is observed that several RDG minima are located at the meeting point of CP trajectories initiated in the unsmoothed ED distribution. At high smoothing levels, the accumulation of ED charges at the ligand–protein interface progressively emerges and is detected through the study of the Laplacian values at the CPs and RDG minima. In parallel, the distance-dependency of the LPED values is less and less clear while the density-dependency is favored. The CP networks and their descriptors are seen as a signature of the ligand–protein arrangement, which is proposed to be further used in the characterization of ligand–protein stackings obtained from, e.g., crystal structures, docking calculations, Molecular Dynamics simulations, and pharmacophore designs. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Compared to conventional linear and circular segments, the parametric curve has advantages in approximating and machining, guaranteeing higher machining precision and better machining quality. Therefore, in Computer Numerical Control (CNC) systems, parametric toolpath has become more and more popular for its high-performance in practical machining and the performance of the parametric interpolator has become a standard to illustrate the advanced CNC systems. In this paper, adaptive-feedrate planning and the iterative interpolator have been developed to generate sampling points with respect to error and higher order kinematic constraints. Firstly, a jerk-limited feedrate profile and look-ahead algorithm are utilized to provide reachable feedrate at critical points. Afterwards, normal jerk (i.e. the jerk in a normal direction) are limited to improve machining precision and quality. In theory, it is proved that the normal jerk limitations have relationship with curvature derivative and a novel iterative interpolator is proposed to ensure the normal jerk limitation by considering the corresponding constraints at curvature derivative extreme points. Finally, simulation and experiments are conducted to demonstrate the efficiency and contour performance of the proposed method compared to conventional method and time-optimal method. [ABSTRACT FROM AUTHOR]

We carry out complete membership to Kaplan classes of certain class of finite products with all zeros on unit circle. In this way we extend Sheil-Small's, Jahangiri's and our previous results. An interpretation of the obtained gap condition in terms of mass and density is given. [ABSTRACT FROM AUTHOR]

The Nazarov–Sodin constant describes the average number of nodal set components of smooth Gaussian fields on large scales. We generalise this to a functional describing the corresponding number of level set components for arbitrary levels. Using results from Morse theory, we express this functional as an integral over the level densities of different types of critical points, and as a result deduce the absolute continuity of the functional as the level varies. We further give upper and lower bounds showing that the functional is at least bimodal for certain isotropic fields, including the important special case of the random plane wave. [ABSTRACT FROM AUTHOR]

In this paper, we study the multiplicity of weak solutions to the boundary value problem − G α u = f (x , y , u) + g (x , y , u) in Ω , u = 0 on ∂ Ω , where Ω is a bounded domain with smooth boundary in R N (N ≥ 2) , α ∈ N , f (x , y , ξ) is odd in ξ and g (x , y , ξ) is a perturbation term. Under some growth conditions on f and g, we show that there are infinitely many weak solutions to the problem. Here we do not require that f satisfies the Ambrosetti-Rabinowitz (AR) condition. The conditions on f and g are relatively weak and our result is new even in the case α = 0 , i.e. for the classical Laplace equation with the Dirichlet boundary condition. [ABSTRACT FROM AUTHOR]

In this paper, a relationship between the zeros and critical points of a polynomial p(z) is established. The relationship is used to prove Sendov's conjecture in some special cases. [ABSTRACT FROM AUTHOR]

In this article, we are interested in the existence of infinitely many solutions for a class of fractional Hamiltonian systems ... where L(t) is neither uniformly positive definite nor coercive, and W(t,x) is locally defined and subquadratic or superquadratic near the origin with respect to x . The proof is based on variational methods and critical point theory. [ABSTRACT FROM AUTHOR]

The inaugural speech of the new President of The United States is one of those rare cases in news translation in which it is possible to identify a Source Text (ST) and compare it to several Target Texts (TTs). This paper focuses on what was reported in eight Italian national daily newspapers concerning the inaugural address of Donald Trump in 2017 on the day following his inaugural address. It provides an overview of the different choices and levels of translation visibility that were observed in the selected newspapers, observing full translations, paratexts and migrated segments embedded in articles describing the inaugural. Through a focus on the ST-TT comparison – employing Selective Appropriation (Valdeón, 2008) and Munday’s Evaluation paradigm (2012) – this investigation shows how the comparative analysis of translations can also be employed to enrich the textual analysis of the inaugural itself. Ideological translation choices are explored, focusing in particular on a case of omission in the right-wing Libero – which openly appreciated the election of Trump – and a case of addition in the communist Il Manifesto – which openly deplored Trump.

The article investigates the Sturm–Liouville problem with one classical and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures for various values of parameter ξ.

We state the product formulae of the values of the levels of functions at critical points involved in asymptotic behaviors of hypergeometric integrals associated with symmetric arrangements of three-dimensional spheres. We show, in an explicit way, how the product of the Hessian, regarding the level functions at all critical points, is related to the behavior of its critical points. We also state two conjectures concerning the same problem associated with general hypersphere arrangements.

In this paper, we are focusing to the following Schrödinger–Maxwell system: \begin{equation} \begin{cases} -\Delta_{g}u+\beta(x)u+eu\phi=\Psi(\lambda,x)f(u) & \mbox{in} \ M,\\ -\Delta_{g}\phi+\phi=qu^{2} & \mbox{in} \ M, \end{cases}\tag{$\mathcal{SM}_{\Psi(\lambda,\cdot)}^{e}$} \end{equation} where $(M,g)$ is a 3-dimensional compact Riemannian manifold without boundary, $e,q>0$ are positive numbers, $f:\mathbb{R}\to\mathbb{R}$ is a continuous function, $\beta\in C^{\infty}(M)$ and $\Psi\in C^{\infty}(\mathbb{R}_{+}\times M)$ are positive functions. By various variational approaches, existence of multiple solutions of the problem $(\mathcal{SM}_{\Psi(\lambda,\cdot)}^{e})$ is established.

In this paper, we establish the existence and multiplicity of solutions for a class of superlinear elliptic systems without Ambrosetti and Rabinowitz growth condition. Our results are based on minimax methods in critical point theory.

The studied area is part of the Balta Ialomiţei hydrographical system and belongs to the lower sector of the Danube, being characterized by the many branches, secondary branches with islets between them, indicating a state of hydro morphological instability of the riverbed. The sector analyzed in this paper is between the bifurcations with the Bala branch (Turcescu Islet) from km 345 and up to Vadu Oii, at the bifurcation with Borcea branch, at km 241.The hydrographic changes that occurred over time in the hydrographic nodes Danube-Bala and Danube Borcea branch, have significantly affected the morph hydrography of the secondary branches. Thus, in the Bala-Danube bifurcation area, the consequences of riverbed changes were reverberated by increasing the takeover capacity of water by Bala branch to the detriment of Danube branch. This leads to a decrease in depths on the Danube branch at low waters, endangering the optimal depths for navigation, the occurrence of critical points for navigation downstream, changes of islets and the main elements of riverbed. Thus, along the analyzed range, the number of islets present in the riverbed of the Danube decreased between 1908 and 1960, remaining constant and with minor changes until 1990, after which there was a consistent increase of the number of islets until the end of the study period in 2016.Also, it find an increase in the total length of the islets and also changes in their geometry and position, especially at the smallest of them.

The paper studies existence of solutions for the nonlinear Schrödinger equation (0.1) − (∇ + i A (x)) 2 u + V (x) u = f (| u |) u with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic Sobolev space. [ABSTRACT FROM AUTHOR]

In this paper, the thermodynamics of Reissner–Nordström-anti de Sitter black hole surrounded by quintessence is studied and the impact of the Gauss–Bonnet term is measured. The modified entropy, first law of thermodynamics and corresponding Smarr relation are derived due to the combined action of the Gauss–Bonnet term and quintessence fluid. We study the so-called black hole chemistry from the analysis of the corresponding equation-of-state, conjugate potential and the critical points in the extended phase space. To study the phase transitions, we plotted P − v , T − v and G − T diagrams and analyzed the conditions for the coexistence of phases. [ABSTRACT FROM AUTHOR]

In recent decades in high industrialised countries the occupational risks and energy costs of labour have decreased while the subjective nutritional and metabolic risk of workers has increased because they often follow an incorrect lifestyle. This article addresses the multidisciplinary assessment and management of these risks in order to define a Nutrient Hazard Analysis and Critical Control Point at Work (NACCPW), specifically dedicated to proper nutrition, which workers must take over before or during the work schedule. It describes the various steps that the professionals concerned will need to develop to define the work-related and subjective metabolic and nutritional critical points and their corrective actions. NACCPW allows to balance work-related metabolic risk with subjective nutritional risk of workers and gives indications to reduce both. The further improvement in working conditions and lifestyle, with a focus on the nutrition of workers, will help to prevent cardio-vascular, metabolic and cancer diseases still very common in Western countries. The effectiveness of NACCPW is ensured by the possibility of including it in periodic health surveillance, which is required by law, for the entire working life. [ABSTRACT FROM AUTHOR]

We obtain new existence of multiple nontrivial M-periodic solutions for a class of second-order discrete Hamiltonian system with the force F(t, x) being neither supquadratic nor subquadratic growth in x. Moreover, we exhibit four instructive examples to illustrate our results. [ABSTRACT FROM AUTHOR]

A general theorem concerning the three critical points for some classes of coercive functionals depending on a real parameter is established, which may derive existence's results of three solutions with various sufficient conditions for some classes of two-point semi-linear boundary value problems. Moreover, by applying known three existence theorems, we derive multiple existence results for a class of quasi-linear differential equation. [ABSTRACT FROM AUTHOR]

Let $p:\mathbb{C}\rightarrow \mathbb{C}$ be a polynomial. The Gauss–Lucas theorem states that its critical points, $p^{\prime }(z)=0$ , are contained in the convex hull of its roots. We prove a stability version whose simplest form is as follows: suppose that $p$ has $n+m$ roots, where $n$ are inside the unit disk, $$\begin{eqnarray}\max _{1\leq i\leq n}|a_{i}|\leq 1~\text{and}~m~\text{are outside}~\min _{n+1\leq i\leq n+m}|a_{i}|\geq d>1+\frac{2m}{n};\end{eqnarray}$$ then $p^{\prime }$ has $n-1$ roots inside the unit disk and $m$ roots at distance at least $(dn-m)/(n+m)>1$ from the origin and the involved constants are sharp. We also discuss a pairing result: in the setting above, for $n$ sufficiently large, each of the $m$ roots has a critical point at distance ${\sim}n^{-1}$. [ABSTRACT FROM AUTHOR]

Copyright of Business Consultant / Poslovni Konsultant is the property of FINconsult Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We give the complete characterization of members of Kaplan classes of products of power functions with all zeros symmetrically distributed in T := fz 2 C : jzj = 1g and weakly monotonic sequence of powers. In this way we extend Sheil-Small's theorem. We apply the obtained result to study univalence of antiderivative of these products of power functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the class of simple dynamical systems on ℝ induced by continuous maps having finitely many non-ordinary points. We characterize this class using labeled digraphs and dynamically independent sets. In fact, we classify dynamical systems up to their number of non-ordinary points. In particular, we discuss about the class of continuous maps having unique non-ordinary point, and the class of continuous maps having exactly two non-ordinary points. [ABSTRACT FROM AUTHOR]

Data and the significance represent sequential structures for scientific relevance. The purpose of the study was to identify epistemological barriers in the architecture to data and the significance of the predictive model of science. The study was carried from January to July 2020, selecting 100 randomized Scopus articles through a random probabilistic sampling, using the ScienceDirect platform as a scientific search tool. Sequential structures were compared using the t-Student test, the results being considered significant with a confidence level of 95% and where differences were found between them (t = -53.88; p = 7.09). It was observed that the analysis for the data was less relevant compared to the importance attributed to its significance. It was concluded that the identification of the epistemological barriers for the architecture to data and the significance in the predictive model of science represents a guide to consider for the measurement of the variables and their interpretation towards scientific knowledge. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point c , which is degenerate, of a multivariate polynomial function f. To this end, we introduce the definition of faithful radius of c by means of the curve of tangency of f. We show that the type of c can be determined by the global extrema of f over the Euclidean ball centered at c with a faithful radius. We propose algorithms to compute faithful radius of c and determine its type. [ABSTRACT FROM AUTHOR]

In this paper, we construct and implement a new improvement of third order weighted essentially non-oscillatory (WENO) scheme in the finite difference framework for hyperbolic conservation laws. In our approach, a modification in the global smoothness measurement is reported by applying all three points on global stencil (i - 1 , i , i + 1) which is used for convergence of non-linear weights towards the optimal weights at critical points and achieves the desired order of accuracy for third order WENO scheme. We use the third order accurate total variation diminishing (TVD) Runge-Kutta time stepping method. The major advantage of the proposed scheme is its better numerical accuracy in smooth regions. The computational performance of the proposed WENO scheme with this global smoothness measurement is verified in several benchmark one- and two-dimensional test cases for scalar and vector hyperbolic equations. Extensive computational results confirm that the new proposed scheme achieves better performance as compared with WENO-JS3, WENO-Z3 and WENO-F3 schemes. [ABSTRACT FROM AUTHOR]

Snap-through phenomenon widely occurs for elastic systems, where the systems lose stability at critical points. Here snap-through of an elastica under bilateral displacement control at a material point is studied, by regarding the whole elastica as two components, i.e., pinned-clamped elasticas. Specifically, stiffness−curvature curves of two pinned-clamped elasticas are firstly efficiently located based on the second-order mode, which are used to determine the shapes of two components. Similar transformations are used to assemble two components together to form the whole elastica, which reveals four kinds of shapes. One advantage of this way compared with other methods such as the shooting method is that multiple coexisting solutions can be located accurately. On the load−deflection curves, four branches correspond to four kinds of shapes and first two branches are symmetrical to the last two branches relative to the original point. For the bilateral displacement control, the critical points can only appear at saddle-node bifurcations, which is different to that for the unilateral displacement control. Specifically, one critical point is found on the first branch and two critical points are found on the secondary branch. In addition, the snap-through among different branches can be well explained with these critical points. [ABSTRACT FROM AUTHOR]

In this paper, we construct some solutions of an elliptic PDE with a supercritical exponent nonlinearity. We follow the ideas of Bahri–Li–Rey (Calc Var Partial Differ Equ V.3:67–93, 1995) by using the finite dimensional reduction. [ABSTRACT FROM AUTHOR]

We study here the random fluctuations in the number of critical points with values in an interval I ⊂ R for Gaussian spherical eigenfunctions f ℓ , in the high energy regime where ℓ → ∞. We show that these fluctuations are asymptotically equivalent to the centred L 2 -norm of f ℓ times the integral of a (simple and fully explicit) function over the interval under consideration. We discuss also the relationships between these results and the asymptotic behaviour of other geometric functionals on the excursion sets of random spherical harmonics. [ABSTRACT FROM AUTHOR]

The inaugural speech of the new President of The United States is one of those rare cases in news translation in which it is possible to identify a Source Text (ST) and compare it to several Target Texts (TTs). This paper focuses on what was reported in eight Italian national daily newspapers concerning the inaugural address of Donald Trump in 2017 on the day following his inaugural address. It provides an overview of the different choices and levels of translation visibility that were observed in the selected newspapers, observing full translations, paratexts and migrated segments embedded in articles describing the inaugural. Through a focus on the ST-TT comparison - employing Selective Appropriation (Valdeón, 2008) and Munday's Evaluation paradigm (2012) - this investigation shows how the comparative analysis of translations can also be employed to enrich the textual analysis of the inaugural itself. Ideological translation choices are explored, focusing in particular on a case of omission in the right-wing Libero - which openly appreciated the election of Trump - and a case of addition in the communist Il Manifesto - which openly deplored Trump. [ABSTRACT FROM AUTHOR]

In this paper we use variational methods and fixed point theorems to study the existence of solutions to a boundary value problem for impulsive differential equations with nonlinear dependence on the derivative. [ABSTRACT FROM AUTHOR]

In this article, a class of step up test procedures for testing the homogeneity of scale parameters from k k ≥ 1 normal populations with that of control population is proposed using sample quasi ranges. A recursive algorithm is used to compute the critical constants that are required for implementing the proposed procedures. Simulation studies have shown that the proposed procedures are better than the existing competitors and are robust when outliers are present. The proposed procedure is illustrated using a real data example. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the existence of at least one nontrivial weak solution for equations involving the (p (·) , q (·)) -Laplace operator. The approach is variational and based on the critical point theory. [ABSTRACT FROM AUTHOR]

In this work we present a novel method to evaluate the liquid–vapour critical temperature using a generalisation of the Microcanonical-ensemble computer simulation method. The isotherms of the chemical potential vs. densities are obtained for a square-well fluid with interaction range λ / σ = 1.5 : From these curves we extracted the critical temperature for different system sizes observing the change of the slope on the curves of the chemical potential in the critical region as function of the temperature. Working with different systems sizes and Finite Size Scaling Theory the critical temperature T c = 1.2180 (29) and the critical exponent ν = 0.65 (3) are obtained, without previous knowledge of T c or ν. These results are in good agreement with the reported values for this system. [ABSTRACT FROM AUTHOR]

The article presents the overview of the main technological processes in fish structured products dehydration. The rational modes of the technological process of minced fish raw materials with various initial moisture and fat content heat treatment are determined. One of the main tasks of the fish processing industry development which allows increasing the profitability of products and their quality is improving technological processes. The scientifically substantiated choice of resource and energy-saving modes of processing food materials is highly important in this case. It will reduce not only production costs but also emissions of harmful substances into the environment and increase the efficiency of using equipment. It must be taken into consideration that the optimization of dehydration technological processes without identifying their patterns is extremely difficult. Increasing efficiency and controlling technological processes makes sense only on the basis of patterns. The effectiveness of the hydrobionts processing determines the quality and cost of finished products manufacturing while fish processing enterprises working. The development and implementation of highly efficient technologies with the use of resource-saving technical systems, for example, using heat pumps, makes it possible to produce cost-effective high-quality products. [ABSTRACT FROM AUTHOR]

The article investigates the Sturm-Liouville problem with one classical and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures for various values of parameter. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the set of critical points of solutions to quasilinear elliptic boundary value problems with Dirichlet null condition on the border of a region convex in one direction, satisfying a symmetry condition. The numberof critical points is estimated by counting the number of connected components of the border having a prescribed unitary tangent vector. [ABSTRACT FROM AUTHOR]

Given a set of points in the complex plane, an incomplete polynomial is defined as one which has these points as zeros except one of them. Recently, the classical result known as Gauss–Lucas theorem on the location of zeros of polynomials and their derivatives was extended to the linear combinations of incomplete polynomials. In this paper, a simple proof of this result is given, and some results concerning the critical points of polynomials due to Jensen and others have extended the linear combinations of incomplete polynomials. [ABSTRACT FROM AUTHOR]