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We correct the proof of Theorem 2 in the mentioned paper concerning finite-difference equilibrium solutions. [ABSTRACT FROM AUTHOR]

This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math. (Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results. [ABSTRACT FROM AUTHOR]

In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced nonlinear second order differential equations with delayed argument in the form x″(t)+q(t)x(τ(t))γsgnx(τ(t))=f(t) in the linear (γ=1) and the superlinear (γ>1) cases. [Copyright &y& Elsevier]

The present paper investigates the following inhomogeneous generalized Hartree equation i u ˙ + Δ u = ± | u | p − 2 | x | b (I α ∗ | u | p | · | b) u , where the wave function is u : = u (t , x) : R × R N → C , with N ≥ 2 . In addition, the exponent b > 0 gives an unbounded inhomogeneous term | x | b and I α ≈ | · | − (N − α) denotes the Riesz-potential for certain 0 < α < N . In this work, our aim is to establish the local existence of solutions in some radial Sobolev spaces, as well as the global existence for small data and the decay of energy sub-critical defocusing global solutions. Our results complement the recent work (Sharp threshold of global well-posedness versus finite time blow-up for a class of inhomogeneous Choquard equations, J. Math. Phys. 60 (2019), 081514). The main challenge in this work is to overcome the singularity of the unbounded inhomogeneous term | x | b for certain b > 0 . [ABSTRACT FROM AUTHOR]

A nonoscillation criterion for a second-order linear difference equation is established correcting a result in [1]. [Copyright &y& Elsevier]

In this paper, we consider a class of Choquard equations with Hardy–Littlewood–Sobolev lower or upper critical exponent in the whole space R N . We combine an argument of L. Jeanjean and H. Tanaka (see (Proc. Am. Math. Soc. 131:2399–2408, 2003) with a concentration–compactness argument, and then we obtain the existence of ground state solutions, which extends and complements the earlier results. [ABSTRACT FROM AUTHOR]

The article discusses research featured in the Expository Research Papers section including one by Laurent Demanet and Lexing Ying on the efficient representations for functions of elliptic operators and another by Jeffrey Blanchard, Coralia Cartis and Jared Tanner on restricted isometry property.

Text Let K be a complete, algebraically closed, non-Archimedean valued field, and let ϕ ∈ K ( z ) with deg ⁡ ( ϕ ) ≥ 2 . In this paper we consider the family of functions ord Res ϕ n ( x ) , which measure the resultant of ϕ n at points x in P K 1 , the Berkovich projective line, and show that they converge locally uniformly to the diagonal values of the Arakelov–Green's function g μ ϕ ( x , x ) attached to the canonical measure of ϕ . Following this, we are able to prove an equidistribution result for Rumely's crucial measures ν ϕ n , each of which is a probability measure supported at finitely many points whose weights are determined by dynamical properties of ϕ . Video For a video summary of this paper, please visit https://youtu.be/YCCZD1iwe00 . [ABSTRACT FROM AUTHOR]

In this paper, finite time blow-up property of solutions to a p-Kirchhoff-type parabolic equation with general nonlinearity is considered. Some sufficient conditions are given for the weak solutions to blow up in finite time. An upper bound for the blow-up time is also derived. The results partially generalize some recent ones reported by Han and Li (Comput Math Appl. 2018;75:3283–3297). [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stability of the solutions of a viscoelastic plate equation with a logarithmic nonlinearity. We assume that the relaxation function g satisfies the minimal condition g ′ (t) ≤ − ξ (t) G (g (t)) , where ξ and G satisfy some properties. With this very general assumption on the behavior of g, we establish explicit and general energy decay results from which we can recover the exponential and polynomial rates when G (s) = s p and p covers the full admissible range [ 1 , 2) . Our new results substantially improve and generalize several earlier related results in the literature such as Gorka (Acta Phys. Pol. 40:59–66, 2009), Hiramatsu et al. (J. Cosmol. Astropart. Phys. 2010(06):008, 2010), Han and Wang (Acta Appl. Math. 110(1):195–207, 2010), Messaoudi and Al-Khulaifi (Appl. Math. Lett. 66:16–22, 2017), Mustafa (Math. Methods Appl. Sci. 41(1):192–204, 2018), and Al-Gharabli et al. (Commun. Pure Appl. Anal. 18(1):159–180, 2019). [ABSTRACT FROM AUTHOR]

In the present paper we establish some theorems on the existence of common approximate fixed points for a pair of generalized contractive type mappings with the property that the diameter of the set of common e--fixed points is tending to zero as e tends to zero. [ABSTRACT FROM AUTHOR]

Abstract This paper provides new equivalence theorems for regular chains and regular differential chains, which are generalizations of Ritt's characteristic sets. These theorems focus on regularity properties of elements of residue class rings defined by these chains, which are revealed by resultant computations. New corollaries to these theorems have quite simple formulations. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the following nonlinear waveequation with variable exponents: u t t − div (| ∇ u | r (⋅) − 2 ∇ u) + | u t | m (⋅) − 2 u t = 0. By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m , r and the initial data. We also give two numerical applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The blended solutions are more general than the unblended solutions for polynomial-like iterative equation with multivalued functions. In this paper we study the blended solutions of polynomial-like iterative equation with multivalued functions. [ABSTRACT FROM AUTHOR]

Let F q denote the finite field of order q . In this paper, some new classes of permutation polynomials of the form ( x p m − x + δ ) s + x over F p 2 m are obtained by determining the number of solutions of certain equations. [ABSTRACT FROM AUTHOR]

In this paper, we show that a Sasakian manifold which also satisfies the generalised gradient Ricci soliton equation, satisfying some conditions, is necessarily Einstein. [ABSTRACT FROM AUTHOR]

Text We develop geometric methods to study the generating weights of free modules of vector-valued modular forms of half-integral weight, taking values in a complex representation of the metaplectic group. We then compute the generating weights for modular forms taking values in the Weil representation attached to cyclic quadratic modules of order 2 p r , where p ≥ 5 is a prime. We also show that the generating weights approach a simple limiting distribution as p grows, or as r grows and p remains fixed. Video For a video summary of this paper, please visit https://youtu.be/QNbPSXXKot4 . [ABSTRACT FROM AUTHOR]

A ring R is said to be left uniquely generated if R a = R b in R implies that a = u b for some unit u in R . These rings have been of interest since Kaplansky introduced them in 1949 in his classic study of elementary divisors. Writing l ( b ) = { r ∈ R | r b = 0 } , a theorem of Canfell asserts that R is left uniquely generated if and only if, whenever R a + l ( b ) = R where a , b ∈ R , then a − u ∈ l ( b ) for some unit u in R . By analogy with the stable range 1 condition we call a ring with this property left annihilator-stable. In this paper we exploit this perspective on the left UG rings to construct new examples and derive new results. For example, writing J for the Jacobson radical, we show that a semiregular ring R is left annihilator-stable if and only if R / J is unit-regular, an analogue of Bass' theorem that semilocal rings have stable range 1. [ABSTRACT FROM AUTHOR]

This paper proposes a kinematics model with four noncoplanar points’ Cartesian coordinates for a spatial parallel manipulator, which is called the tetrahedron coordinate method. The sufficient and necessary criteria of utilizing the Cartesian coordinates of the four noncoplanar points are proved. Because the constraint equations are either quadratic or linear, and the coordinates are complete Cartesian, the derivative matrix of the constraint equations only consists of linear or constant elements that are the advantages of the general natural coordinate method as well. However, the number of variables of the general natural coordinate method will increase with the increasing number of investigated points. The tetrahedron coordinate approach proposed in this paper does not need to induce any new variables when more points on the manipulator are considered. As a result, it has a prevailing advantage over the general natural coordinate method. This advantage is especially explicit when establishing the kinematics models for complex spatial parallel manipulators with three to six degrees of freedom, the virtues of which are demonstrated by a case study. [ABSTRACT FROM PUBLISHER]

This paper experimentally demonstrates the use of a microstrip reflectarray as a low-profile planar substitute to a conic section subreflector (hyperboloidal type) in a symmetric dual reflector system at Ku-band. At first, a brief discussion on the simulation and measurement techniques utilized in the paper is provided. A nominal dual reflector Cassegrain system is synthesized through simulations where a feed horn is used to illuminate the hyperboloidal subreflector. Next, a flat metallic subreflector is placed at the subreflector location. This is a critical task as it shows the importance of phase compensation. Due to the flat subreflector, the feed is defocused from the image of the focus and creates phase aberration, leading to beam bifurcation, pattern degradation, and performance deterioration of the dual reflector system. A planar microstrip patch-type subreflectarray is then designed to mimic a hyperboloidal subreflector. Ray tracing is applied to the subreflector-feed system to calculate the phase needed to compensate for the axial defocusing of the feed. A prototype subreflectarray based on the ray-optics approach is fabricated. Radiation pattern measurements and back-projection holographic diagnostics demonstrate that the subreflectarray acts as a hyperboloidal subreflector and restores the antenna performance with a well-defined main beam and low side lobes. [ABSTRACT FROM PUBLISHER]

In this paper, a new construction of zero-difference balanced functions defined on \BBZv is given, where v is an odd positive integer. Based on the generic constructions proposed by Ding, optimal constant composition codes and perfect difference systems of sets with new parameters can be generated from the zero-difference balanced functions constructed in this paper. [ABSTRACT FROM AUTHOR]

Two words u and v are k -abelian equivalent if for each word x of length at most k , x occurs equally many times as a factor in both u and v . The notion of k -abelian equivalence is an intermediate notion between the abelian equivalence and the equality of words. In this paper, we study the equivalence classes induced by the k -abelian equivalence, mainly focusing on the cardinalities of the classes. In particular, we are interested in the number of singleton k -abelian classes, i.e., classes containing only one element. We find a connection between the singleton classes and cycle decompositions of the de Bruijn graph. We show that the number of classes of words of length n containing one single element is of order O ( n N m ( k − 1 ) − 1 ) , where N m ( l ) = 1 l ∑ d | l φ ( d ) m l / d is the number of necklaces of length l over an m -ary alphabet. We conjecture that the upper bound is sharp. We also remark that, for k even and m = 2 , the lower bound Ω ( n N m ( k − 1 ) − 1 ) follows from an old conjecture on the existence of Gray codes for necklaces of odd length. We verify this conjecture for necklaces of length up to 15. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a procedure used in the assessment of the real heat transfer characteristic of shell and tube and plate heat exchangers. The theoretical fundamentals of the procedure are introduced as well as the measured data collection and processing. The theoretical analysis is focused on the adoption of criterial equations which, subjected to certain verification criteria presented in the paper, provide the most credible value of the convection heat transfer coefficients inside the circular and flat tubes. In the end two case studies are presented, one concerning a shell and tube heat exchanger operational at INCERC Thermal Substation and the other concerning a plate heat exchanger tested on the Laboratory Stand of the Department of Building Services and Efficient Use of Energy in Buildings of INCERC Bucharest. [ABSTRACT FROM AUTHOR]

Abstract: One of the particularities of information encoded as DNA strands is that a string u contains basically the same information as its Watson–Crick complement, denoted here as . Thus, any expression consisting of repetitions of u and can be considered in some sense periodic. In this paper, we give a generalization of Lyndon and Schützenberger’s classical result about equations of the form , to cases where both sides involve repetitions of words as well as their complements. Our main results show that, for such extended equations, if , then all three words involved can be expressed in terms of a common word t and its complement . Moreover, if , then is an optimal bound. These results are established based on a complete characterization of all possible overlaps between two expressions that involve only some word u and its complement , which is also obtained in this paper. [Copyright &y& Elsevier]

This paper handles the problem of accuracy loss for flow solutions on computational domains with a heterogeneous discretization on the subdomains. The problem occurs, e.g., when a composite multiblock mesh comprises blocks with different grid resolutions on the common boundary face. The problem is especially troublesome for high-accuracy solutions, in which tailoring of heterogeneous meshes frequently brings the loss of accuracy on a global scale. This paper focuses on the treatment of non-point-to-point structured multiblock grids, in which face-matched block boundaries are not necessarily point-matched. In the context of high-accuracy characteristic finite volume schemes for three-dimensional Navier-Stokes equations, a new approach is proposed that handles composite grids without the need in geometrical adjustment of boundary cells or any other grid-related preprocessing. In the proposed approach, interblock cell clusters are formed that contain boundary cells from the neighboring blocks of different resolutions. For each such cluster, the residuals of the Navier-Stokes equations are computed and then distributed among the cells of the host cluster by directly minimizing the flux imbalance in an appropriate norm. Outside these clusters, the residuals are computed in the regular way. The method allows automatic preservation of the conservative property of fluxes by placing constraints upon the optimum, it does not change the stability properties of the basic high-accuracy scheme and ensures a sufficiently high level of approximation on grids with reduced resolution. The results that include a number of numerical tests for two- and three-dimensional wings indicate good accuracy and robustness of the method and its applicability to full-scale Navier-Stokes computations. [ABSTRACT FROM AUTHOR]

This paper describes a design for a least mean square error estimator in discrete time systems where the components of the state vector, in measurement equation, are corrupted by different multiplicative noises in addition to observation noise. We show how known results can be considered a particular case of the algorithm stated in this paper. [ABSTRACT FROM AUTHOR]

Surface roughness is often considered the main purpose in contemporary computer numerical controlled (CNC) machining industry. Most existing optimization researches for CNC finish turning were either accomplished within certain manufacturing circumstances or achieved through numerous equipment operations. Therefore, a general deduction optimization scheme is deemed to be necessary for the industry. In this paper, the cutting depth, feed rate, speed, and tool nose runoff with low, medium, and high level are considered to optimize the surface roughness for finish turning based on L9(34) orthogonal array. Additionally, nine fuzzy control rules using triangle membership function with respective to five linguistic grades for surface roughness are constructed. Considering four input and twenty output intervals, the defuzzification using center of gravity is then completed. Thus, the optimum general fuzzy linguistic parameters can then be received. The confirmation experiment result showed that the surface roughness from the fuzzy linguistic optimization parameters is significantly advanced compared to that from the benchmark. This paper certainly proposes a general optimization scheme using orthogonal array fuzzy linguistic approach to the surface roughness for CNC turning with profound insight. [ABSTRACT FROM AUTHOR]

Suppose that X 1,..., X n is a sequence of independent random vectors, identically distributed as a d-dimensional random vector X. Let be a parameter of interest and be some nuisance parameter. The unknown, true parameters ( μ 0, ν 0) are uniquely determined by the system of equations E{ g( X, μ 0, ν 0)} = 0, where g = ( g 1,..., g p+ q) is a vector of p+ q functions. In this paper we develop an empirical likelihood (EL) method to do inference for the parameter μ 0. The results in this paper are valid under very mild conditions on the vector of criterion functions g. In particular, we do not require that g 1,..., g p+ q are smooth in μ or ν. This offers the advantage that the criterion function may involve indicators, which are encountered when considering, e.g. differences of quantiles, copulas, ROC curves, to mention just a few examples. We prove the asymptotic limit of the empirical log-likelihood ratio, and carry out a small simulation study to test the performance of the proposed EL method for small samples. [ABSTRACT FROM AUTHOR]

An epicycloid or hypocycloid mechanism is capable of drawing an exact epicycloid or hypocycloid curve. Similar mechanism designs can be found abundantly in industrial machines or educational equipments. Currently, the major type of epicycloid or hypocycloid configurations is planetary gear trains, which contain a binary link that has one fixed and one moving pivot, and a singular link adjacent to the moving pivot. The main feature of the configurations is that a point on the singular link may describe an epicycloid or hypocycloid curve when the binary link is rotated. The main aim of this paper is to develop a new design method in designing new configurations of planetary epicycloid (hypocycloid) mechanisms. This paper analyses the characteristics of the topological structures of existing planetary gear train type epicycloid (hypocycloid) mechanisms. The motion equations and kinematical model of the mechanism were derived and appropriate design constraints and criteria were implemented. Finally, using the design constraints and criteria, this work designs new epicycloid (hypocycloid) mechanisms. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the study begun in the previous paper with the same title. We analyze ER(2)16*+8(RP2n) and compute ER(2)*(RP16K+1), and use these to prove more nonimmersion theorems for RPn, including many in fairly low dimensions. In particular, we get 12 new nonimmersion results for RPn where n < 192, the range included in the tables Don Davis keeps. These complement the 10 already found in the first paper. [ABSTRACT FROM AUTHOR]

This paper is a companion to the Boardman-Wilson paper on the ring spectrum P(n). When the prime is 2, this spectrum is not commutative, which introduces several complications. Here, we supply the necessary details of the relevant Hopf algebroids and Hopf ring for this case. [ABSTRACT FROM AUTHOR]

In this paper we establish Hyers--Ulam--Rassias stability of the fol- lowing quadratic mapping of Apollonius type (1) Q(z - x) + Q(z - y) = ½ Q(x - y) + 2Q(z - x + y)/2) in non-Archimedean spaces. The term Hyers-Ulam-Rassias stability is due to the seminal paper: Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300. [ABSTRACT FROM AUTHOR]

In this paper, we present a Newton-type method for a class of mathematical programs with complementarity constraints. Under the MPEC-LICQ, we use the definition of B-stationary point to construct a constrained equations model, and apply the Newton method to solve the problem. At the end of this paper, numerical results are reported to show our method's validity. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to build sequences of suitably smooth approximate solutions to the Saint-Venant model that preserve the mathematical structure discovered in [D. Bresch, B. Desjardins, Comm. Math. Phys. 238 (1–2) (2003) 211–223]. The stability arguments in this paper then apply to such sequences of approximate solutions, which leads to the global existence of weak solutions for this model. Extension of this mollifying procedure to the case of compressible Navier–Stokes equations is also provided. Using the recent paper written by the authors, this provides global existence results of weak solutions for the barotropic Navier–Stokes equations and for compressible Navier–Stokes equations with heat conduction using a particular cold pressure term close to vacuum. [Copyright &y& Elsevier]

The present note is an addendum to our previous article ‘On a general Thue's equation.’ Corollary 2 in that paper provides a lower bound for the values of a polynomial with algebraic coefficients at integral points. Our purpose here is to prove a stronger version of it; also, we slightly simplify its proof, avoiding the use of Theorem 3 in the original paper. [ABSTRACT FROM AUTHOR]

The concept of the ‘relation of comparability’ was introduced by Maillet in [7], who showed that if α,β are comparable Liouville numbers then each of the numbers α+β, α-β, αβ and α/β is either a rational or Lioville number. Moreover those which are Liouville numbers are comparable aamong theem and toα and β Maillet's proof uses in an essential way the transitivity of the comparability relation. Unfortunately, as the comparability relation is not transitive, his proof is defective. In this paper, without using the comparability relation, we obtain some uncountable subfields of p-adic numbers field, Qp. In [1] using a different notion of comparability, Alnıaçık was able to define some uncountable subfields of C. In this paper, without using comparability relation, we define irregular semistrong p-adic Um numbers and obtain some uncountable subfields of p-adic numbers field Qp. [ABSTRACT FROM AUTHOR]

In the first part of this paper we study the regularity properties of solutions of initial- or boundary-value problems of linear Fredholm integro-differential equations with weakly singular or other nonsmooth kernels. We then use these results in the analysis of a piecewise polynomial collocation method for solving such problems numerically. The main purpose of the paper is the derivation of optimal global convergence estimates and the analysis of the attainable order of convergence of numerical solutions for all values of the nonuniformity parameter of the underlying grid. [ABSTRACT FROM AUTHOR]

Abstract: The present paper describes an efficient algorithm to integrate the equations of motion implicitly in the frequency domain. The standard FEM displacement model (Galerkin formulation) is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green’s function of the mechanical system in nodal coordinates. In the present formulation, mechanical system Green’s functions are implicitly calculated in the frequency domain. Once the Green’s functions related matrices are computed, a time integration procedure, which demands low computational effort when applied to non-linear mechanical systems, becomes available. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach. [Copyright &y& Elsevier]

A novel method is proposed in this paper for automatic acquisition of three-dimensional (3-D) models of unknown objects by an active vision system, in which the vision sensor is to be moved from one viewpoint to the next around the target to obtain its complete model. In each step, sensing parameters are determined automatically for incrementally building the 3-D target models. The method is developed by analyzing the target's trend surface, which is the regional feature of a surface for describing the global tendency of change. While previous approaches to trend analysis are usually focused on generating polynomial equations for interpreting regression surfaces in three dimensions, this paper proposes a new mathematical model for predicting the unknown area of the object surface. A uniform surface model is established by analyzing the surface curvatures. Furthermore, a criterion is defined to determine the exploration direction, and an algorithm is developed for determining the parameters of the next view. Implementation of the method is carried out to validate the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a numerical study of noise source term in non-isothermal flows in the context of an aeroacoustic hybrid technique at low Mach numbers. Asymptotic analysis applied to the fully compressible Navier–Stokes equations provides separated sets of equations for the dynamic of the flow and the production and propagation of acoustic waves. Comparisons with analytical dipole and quadrupole distributions are performed, confirming the dipole type of non-isothermal source distribution. This paper is a preliminary work for some more extensive studies on the topic. To cite this article: F. Golanski, C. Prax, C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models. [Copyright &y& Elsevier]

In this paper, we study the behavior of solutions of a semilinear elliptic equation in the exterior of a compact set as $|x|\backslash to\; \backslash nomathbreak\; \backslash infty$. Such equations were considered by many authors (for example, Kondrat'ev, Landis, Oleinik, Veron, etc.). In the present paper, we study the case in which in the equation contains lower terms. The coefficients of the lower terms are arbitrary bounded measurable functions. It is shown that the solutions of the equation tend to zero as $|x|\backslash to\; \backslash nomathbreak\; \backslash infty$. [ABSTRACT FROM AUTHOR]

In many applications, it is useful to know how the solution to a set of simultaneous linear equations depends on parameters entering into the coefficients. To this end, this paper addresses the classical equation with matrix and vector depending on an -tuple of parameters with components entering in a rank-one manner. Given such a system, the following problems are considered: For solution component and parameter , determine if the first and second order partial derivatives of with respect to are of one sign for all in a prescribed hypercube of radius ; i.e., we determine which components enter the solution either monotonically, convexly or concavely. In this paper, we provide extreme point results for these problems. Namely, we need only check the sign of three specially constructed multilinear functions at the extreme points (vertices) of in order to ascertain whether the desired one-sign condition is satisfied over the entire hypercube. Central to the proof of extremality is a special “multilinear factorization” of the partial derivatives of . This leads to a simple method to compute the so-called radii of convexity, concavity and monotonicity. [Copyright &y& Elsevier]

A system that consists of a damped oscillator impacting two immovable fenders has been considered in this paper. In the first part a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples. In the second part of the paper, the results of some numerical investigations have been presented. The goal of these studies was to determine, in which regions of parameters characterizing the system, the motion of the oscillator is periodic and stable. [ABSTRACT FROM AUTHOR]

This paper deals with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equation by employing the fixed-point theorem in cones. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results. [Copyright &y& Elsevier]

In two previous papers, the two first-named authors introduced a notion of contact r-surgery along Legendrian knots in contact 3-manifolds. They also showed how (at least in principle) to convert any contact r-surgery into a sequence of contact (± 1)-surgeries, and used this to prove that any (closed) contact 3-manifold can be obtained from the standard contact structure on S3 by a sequence of such contact (± 1)-surgeries. In the present paper, we give a shorter proof of that result and a more explicit algorithm for turning a contact r-surgery into (± 1)-surgeries. We use this to give explicit surgery diagrams for all contact structures on S3 and S1 x S2, as well as all overtwisted contact structures on arbitrary closed, orientable 3-manifolds. This amounts to a new proof of the Lutz-Martinet theorem that each homotopy class of 2-plane fields on such a manifold is represented by a contact structure. [ABSTRACT FROM AUTHOR]

We prove that the equation x2 − kxy + y2 + x = 0 with k ∊ N+ has an infinite number of positive integer solutions x and y if and only if k = 3. For k = 3 the quotient SHAPE="SOL" ALIGN="C" STYLE="S">xy is asymptotically equal to (3 + √5)/2 or (3 − √5)/2. Results of the paper are based on data obtained via Computer Algebra System (derive 5). Some derive procedures presented in the paper made it possible to discover interesting regularities concerning simple continued fractions of certain numbers. [Copyright &y& Elsevier]

In this paper conditions are derived for the existence of a common solution X to the matrix equations AiXBj=Cij,(i,j)∈Γ, where the matrices Ai,Bj,Cij and X have suitable dimensions and the (i,j)’s are index pairs in some set Γ. The purpose of this paper is to present, for certain specific sets of index pairs Γ, verifiable necessary and sufficient solvability conditions that are stated directly in terms of the matrices and that do not use Kronecker products. [Copyright &y& Elsevier]