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In this paper, we show that the hyperstability of the general linear equation recently proved by Piszczek (Aequationes Math 88:163–168, 2014) is a direct consequence of that of the Cauchy equation proved earlier by Brzdȩk (Acta Math Hung 141:58–67, 2013). [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the global stability of the solutions, the boundedness and the periodic character of the nonlinear difference equation xn+1 = αxn+βxn-l+γxn-k + axnxn-k/bxn + cxn-l + dxn-k, n = 0, 1, ..., where the parameters α, β, γ, a, b, c and d are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, x0 are positive real numbers where s = max{l, k}. Some numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

The stabilization problem of state observer based for linear discrete-time periodic (LDP) system and its robust consideration are discussed in this paper. It is proved that the periodic controller and the full-dimensional periodic state observer can be designed separately. Based on the well-known CGalgorithm for matrix equation Ax = b as well as applying the lifting technique and algebraic operations, an iterative algorithm for both periodic observer gains and periodic state feedback gains can be generated simultaneously. By optimizing the free parameter matrix in the proposed algorithm, a robust stabilization algorithm based on periodic observer for LDP systems is presented. One numerical example is worked out to illustrate the effect of the proposed approaches. [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 prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients. More precisely, we deal with coefficients and right hand sides (RHS) in Lq with q ≥ n . This extends the result of Caffarelli on the C loc 1 , 1 regularity of the convex envelope of supersolutions of fully nonlinear elliptic equations with bounded RHS. Moreover, we also provide a regularity result with estimates for ω -semiconvex functions that are supersolutions to the same type of equations with unbounded RHS (i.e, RHS in L q , q ≥ n ). By a completely different method, our results here extend the recent regularity results obtained by Braga et al. (Adv Math 334:184–242, 2018) for q > n , as far as fully nonlinear PDEs are concerned. These results include, in particular, the apriori estimate obtained by Caffarelli et al. (Commun Pure Appl Math 38(2):209–252, 1985) on the modulus of continuity of the gradient of ω -semiconvex supersolutions (for linear equations and bounded RHS) that have a Hölder modulus of semiconvexity. [ABSTRACT FROM AUTHOR]

In this paper, I generalize Holzer's theorem for semi-diagonal equation. [ABSTRACT FROM AUTHOR]

This paper deals with junction conditions for Hamilton–Jacobi–Bellman (HJB) equations for finite horizon control problems on multi-domains. We consider two different cases where the final cost is continuous or lower semi-continuous. In the continuous case, we extend the results in Z. Rao and H. Zidani, Hamilton-Jacobi-Bellman equations on multi-domains, in Control and Optimization with PDE Constraints, Vol. 164 of International Series of Numerical Mathematics. Birkhäuser, Basel (2013) 93–116. in a more general framework with switching running costs and weaker controllability assumptions. The comparison principle has been established to guarantee the uniqueness and the stability results for the HJB system on such multi-domains. In the lower semi-continuous case, we characterize the value function as the unique lower semi-continuous viscosity solution of the HJB system, under a local controllability assumption. [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]

In this paper, we consider the mth order Cauchy-Euler's differential equation involving a para-Grassmann variable of order p. In the Grassmann case (i.e., p = 1), we determine the solution for arbitrary order m. In the case of arbitrary order p, we give a solution for the cases m = 1, 2. [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]

The book Das Interpretationsproblem der Formalisierten Zahlentheorie und ihre Formale Widerspruchsfreiheit by Erik Stenius published in 1952 contains a consistency proof for infinite ω-arithmetic based on a semantical interpretation. Despite the proof’s reference to semantics the truth definition is in fact equivalent to a syntactical derivability or reduction condition. Based on this reduction condition Stenius proves that the complexity of formulas in a derivation can be limited by the complexity of the conclusion. This independent result can also be proved by cut elimination for ω-arithmetic which was done by Schütte in 1951.In this paper we interpret the syntactic reduction in Stenius’ work as a method for cut elimination based on invertibility of the logical rules. Through this interpretation the constructivity of Stenius’ proof becomes apparent. This improvement was explicitly requested from Stenius by Paul Bernays in private correspondence (In a letter from Bernays begun on the 19th of September 1952 (Stenius & Bernays, 1951–75)). Bernays, who took a deep interest in Stenius’ manuscript, applied the described method in a proof Herbrand’s theorem. In this paper we prove Herbrand’s theorem, as an application of Stenius’ work, based on lecture notes of Bernays (Bernays, 1961). The main result completely resolves Bernays’ suggestions for improvement by eliminating references to Stenius’ semantics and by showing the constructive nature of the proof. A comparison with Schütte’s cut elimination proof shows how Stenius’ simplification of the reduction of universal cut formulas, which in Schütte’s proof requires duplication and repositioning of the cuts, shifts the problematic case of reduction to implications. [ABSTRACT FROM AUTHOR]

Say that two sentences are factually equivalent when they describe the same facts or situations, understood as worldly items, i.e. as bits of reality rather than as representations of reality. The notion of factual equivalence is certainly of central interest to philosophical semantics, but it plays a role in a much wider range of philosophical areas. What is the logic of factual equivalence? This paper attempts to give a partial answer to this question, by providing an answer the following, more specific question: Given a standard propositional language with negation, conjunction and disjunction as primitive operators, which sentences of the language should be taken to be factually equivalent by virtue of their logical form? The system for factual equivalence advocated in this paper is a proper fragment of the first-degree system for the logic of analytic equivalence put forward in the late seventies by R. B. Angell. I provide the system with two semantics, both formulated in terms of the notion of a situation’s being fittingly described by a linguistic item. In the final part of the paper I argue, contra a view I defended in my “Grounding and Truth-Functions” (2010), that the logic for factual equivalence I advocate here should be preferred to Angell’s logic if one wishes to follow the general conception of the relationships between factual equivalence and the notion of grounding put forward in the 2010 paper. [ABSTRACT FROM AUTHOR]

According to propositional contingentism, it is contingent what propositions there are. This paper presents two ways of modeling contingency in what propositions there are using two classes of possible worlds models. The two classes of models are shown to be equivalent as models of contingency in what propositions there are, although they differ as to which other aspects of reality they represent. These constructions are based on recent work by Robert Stalnaker; the aim of this paper is to explain, expand, and, in one aspect, correct Stalnaker’s discussion. [ABSTRACT FROM AUTHOR]

A one-sided limit order book is modeled as a noncooperative game for several players. Agents offer various quantities of an asset at different prices, competing to fulfill an incoming order, whose size is not known a priori. Players can have different payoff functions, reflecting different beliefs about the fundamental value of the asset and probability distribution of the random incoming order. In a previous paper, the existence of a Nash equilibrium was established by means of a fixed point argument. The main issue discussed in the present paper is whether this equilibrium can be obtained from the unique solution to a two-point boundary value problem, for a suitable system of discontinuous ordinary differential equations. Some additional assumptions are introduced, which yield a positive answer. In particular, this is true when there are exactly two players, or when all players assign the same exponential probability distribution to the incoming order. In both of these cases, we also prove that the Nash equilibrium is unique. A counterexample shows that these assumptions cannot be removed, in general. [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 prove the following differential analog of the Noether normalization lemma: for every d-dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map on to the d-dimensional affine space. Equivalently, for every integral differential algebra A over differential field of zero characteristic there exist differentially independent b1, . . . , bd such that A is differentially algebraic over subalgebra B differentially generated by b1, . . . , bd, and whenever p ⊂ B is a prime differential ideal, there exists a prime differential ideal q ⊂ A such that p = B ∩ q. We also prove the analogous theorem for differential algebraic varieties over the ring of formal power series over an algebraically closed differential field and present some applications to differential equations. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods are widely used for solving unconstrained optimization and nonlinear equations, specially in large-scale cases. Since they own the attractive practical factors of simple computation and low memory requirement, interesting theoretical features of curvature information and strong global convergence. In this paper, we present a modified conjugate gradient algorithm by line search method with acceleration scheme for nonlinear symmetric equations. Furthermore, the proposed method not only possess descent property but also owns global convergence in mild conditions. Numerical results also indicate that the presented method is much more effective than the other methods for the test problems. [ABSTRACT FROM PUBLISHER]

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]

In this paper, we compute the general solution and determine the Ulam-Hyers stability for a new form of hexadecic functional equations in multi-Banach spaces. [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]

Purpose – The linear matrix equations have wide applications in engineering, physics, economics and statistics. The purpose of this paper is to introduce iterative methods for solving the systems of linear matrix equations. Design/methodology/approach – According to the hierarchical identification principle, the authors construct alternating direction gradient-based iterative (ADGI) methods to solve systems of linear matrix equations. Findings – The authors propose efficient ADGI methods to solve the systems of linear matrix equations. It is proven that the ADGI methods consistently converge to the solution for any initial matrix. Moreover, the constructed methods are extended for finding the reflexive solution to the systems of linear matrix equations. Originality/value – This paper proposes efficient iterative methods without computing any matrix inverses, vec operator and Kronecker product for finding the solution of the systems of linear matrix equations. [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]

This paper mainly proves the generic properties of the Camassa-Holm equation and the two-component Camassa-Holm equation in a sense of Baire category. We reveal their differences in generic regularity and singular behavior. [ABSTRACT FROM AUTHOR]

This paper is concerned with the spreading (persistence) and vanishing (extinction) of a disease which is characterized by a diffusive SIRS model with a bilinear incidence rate and free boundary. Through discussing the dynamics of a free boundary problem of an SIRS model, the spreading of a disease is described. We get the sufficient conditions which ensure the disease spreading or vanishing. In addition, the estimate of the expanding speed is also given when the free boundaries extend to the whole $$\mathbb {R}$$ . [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]

Purpose |!|#8211; The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro-symmetric and central antisymmetric matrices. Design/methodology/approach |!|#8211; By extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro-symmetric and central antisymmetric matrices. Findings |!|#8211; When the general coupled matrix equations are consistent over the generalized centro-symmetric and central anti-symmetric matrices, the generalized centro-symmetric and central anti-symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti-symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti-symmetric solutions to given generalized centro-symmetric and central anti-symmetric matrices can be obtained by finding the least Frobenius norm generalized centro-symmetric and central anti-symmetric solutions of new matrix equations. The authors employ some numerical examples to support the theoretical results of this paper. Finally, the application of the presented methods is highlighted for solving the projected generalized continuous-time algebraic Lyapunov equations (GCALE). Originality/value |!|#8211; By the algorithms, the solvability of the general coupled matrix equations over generalized centro-symmetric and central anti-symmetric matrices can be determined automatically. The convergence results of the iterative algorithms are also proposed. Several examples and an application are given to show the efficiency of the presented methods. [ABSTRACT FROM AUTHOR]

Purpose |!|#8211; Solving the non-linear equation f(x)=0 has nice applications in various branches of physics and engineering. Sometimes the applications of the numerical methods to solve non-linear equations depending on the second derivatives are restricted in physics and engineering. The purpose of this paper is to propose two new modified Newton|!|#39;s method for solving non-linear equations. Convergence results show that the order of convergence of the proposed iterative methods for a simple root is four. The iterative methods are free from second derivative and can be used for solving non-linear equations without computing the second derivative. Finally, several numerical examples are given to illustrate that proposed iterative algorithms are effective. Design/methodology/approach |!|#8211; In this paper, first the authors introduce two new approximations for the definite integral arising from Newton|!|#39;s theorem. Then by considering these approximations, two new iterative methods are provided with fourth-order convergence which can be used for solving non-linear equations without computing second derivatives. Findings |!|#8211; In this paper, the authors propose two new iterative methods without second derivatives for solving the non-linear equation f(x)=0. From numerical results, it is observed that the new methods are comparable with various iterative methods. Also numerical results corroborate the theoretical analysis. Originality/value |!|#8211; The best property of these schemes is that they are second derivative free. Also from numerical results, it is observed that the new methods are comparable with various iterative methods. The numerical results corroborate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the implicit Runge-Kutta Scheme is derived to solve the NS equations, and its characters of stability, precision and efficiency are studied respectively. Some benchmark cases are calculated to validate the capabilities of the numerical program. The results show that the implicit R-K method given in this paper has high stability, high precision and high efficiency, which make it suitable to compute the unsteady reactive nonequilibrium flow. [ABSTRACT FROM AUTHOR]

This paper is concerned with an ordinary non-linear differential equation that occurs in the theory of thermal explosion and, for the spherically symmetric case, in the theory of stellar structure. For plane and axial symmetry, closed form solutions are well known, but the spherically symmetric case can so far only be obtained numerically. By examining the problem in the phase plane, Enig (1967, Critical parameters in the Poisson-Boltzmann equation of steady-state thermal explosion theory. Combust. Flame, 10, 197–199enig1967 was able to obtain an equation from which the critical parameters of the equations can be determined. The equation is of Abel type and there is some difficulty in determining an integrating factor. We note that the partial differential equation for the integrating factor is more difficult to solve then the original equation. A general method is presented that allows the solution to be found in parametric form. Methods of solution for the spherically symmetric case have been presented by various authors. It is shown that these may all be reduced to the equation of Enig. The spherically symmetric case has been examined in some detail near its singular point. In a brilliant but largely ignored paper, it was Jules Enig who first discovered the existence of a vortex in the phase plane. It is hoped that my contribution has solved some of the mysteries of the vortex. [ABSTRACT FROM PUBLISHER]

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]

Abstract. In this paper, we study domain decomposition preconditioners for multiscale flowsin high-contrast media. We consider flow equations governed by elliptic equations in heterogeneous media with a large contrast in the coefficients. Our main goal is to develop domain decomposition preconditioners with the condition number that is independent of the contrast when there are variations within coarse regions. This is accomplished by designing coarse-scale spaces and interpolators that represent important features of the solution within each coarse region. The important features are characterized by the connectivities of high-conductivity regions. To detect these connectivities, we introduce an eigenvalue problem that automatically detects high-conductivity regions via a large gap in the spectrum. A main observation is that this eigenvalue problem has a few small, asymptotically vanishing eigenvalues. The number of these small eigenvalues is the same as the number of connected high-conductivity regions. The coarse spaces are constructed such that they span eigenfunctions corresponding to these small eigenvalues. These spaces are used within two-level additive Schwarz preconditioners as well as overlapping methods for the Schur complement to design preconditioners. We show that the condition number of the preconditioned systems is independent ofthe contrast. More detailed studies are performed for the case when the high-conductivity region is connected within coarse block neighborhoods. Our numerical experiments confirm the theoretical results presented in this paper. [ABSTRACT FROM AUTHOR]

We establish a logarithmic-type rate of convergence for the homogenization of fully nonlinear uniformly elliptic second-order pde in strongly mixing media with similar, i.e., logarithmic, decorrelation rate. The proof consists of two major steps. The first, which is actually the only place in the paper where probability plays a role, establishes the rate for special (quadratic) data using the methodology developed by the authors and Wang to study the homogenization of nonlinear uniformly elliptic pde in general stationary ergodic random media. The second is a general argument, based on the new notion of δ-viscosity solutions which is introduced in this paper, that shows that rates known for quadratic can be extended to general data. As an application of this we also obtain here rates of convergence for the homogenization in periodic and almost periodic environments. The former is algebraic while the latter depends on the particular equation. [ABSTRACT FROM AUTHOR]

Cholak, Groszek and Slaman proved in J Symb Log 66:881–901, 2001 that there is a nonzero computably enumerable (c.e.) degree cupping every low c.e. degree to a low c.e. degree. In the same paper, they pointed out that every nonzero c.e. degree can cup a low2 c.e. degree to a nonlow2 degree. In Jockusch et al. (Trans Am Math Soc 356:2557–2568, 2004) improved the latter result by showing that every nonzero c.e. degree c is cuppable to a high c.e. degree by a low2 c.e. degree b. It is natural to ask in which subclass of low2 c.e. degrees can b in Jockusch et al. (Trans Am Math Soc 356:2557–2568, 2004) be located. Wu proved in Math Log Quart 50:189–201, 2004 that b can be cappable. We prove in this paper that b in Jockusch, Li and Yang’s result can be noncuppable, improving both Jockusch, Li and Yang, and Wu’s results. [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]

Some preconditioners for accelerating the classical iterative methods are given in Zhang et al. [Y. Zhang and T.Z. Huang, A class of optimal preconditioners and their applications, Proceedings of the Seventh International Conference on Matrix Theory and Its Applications in China, 2006. Y. Zhang, T.Z. Huang, and X.P. Liu, Modified iterative methods for nonnegative matrices and M-matrices linear systems, Comput. Math. Appl. 50 (2005), pp. 1587-1602. Y. Zhang, T.Z. Huang, X.P. Liu, A class of preconditioners based on the (I+S(α))-type preconditioning matrices for solving linear systems, Appl. Math. Comp. 189 (2007), pp. 1737-1748]. Another kind of preconditioners approximating the inverse of a symmetric positive definite matrix was given in Simons and Yao [G. Simons, Y. Yao, Approximating the inverse of a symmetric positive definite matrix, Linear Algebra Appl. 281 (1998), pp. 97-103]. Zhang et al. 's preconditioners and Simons and Yao's are generalized in this paper. These preconditioners are all of low construction cost, which all could be taken as approximate inverse of M-matrices. Numerical experiments of these preconditioners applied with Krylov subspace methods show the effectiveness and performance, which also show that the preconditioners proposed in this paper are better approximate inverse for M-matrices than Simons'. [ABSTRACT FROM AUTHOR]

We found a minor error in the proof of paper “Universal Alignment Probability Revisited” by S.Y. Lin and Y.C. Ho (J. Optim. Theory Appl. 113(2):399–407, ). In this note, we give a counterexample and explain the reason. We also show that the conclusion of that paper is still correct despite this minor error. A new proof of the conclusion is given. [ABSTRACT FROM AUTHOR]