Prime Ideals in Near-Rings

An ideal I of a near-ring R is a type one prime ideal if whenever a Rb ? I, then a ∈ I or b ∈ I. This paper considers the interconnections between prime ideals and type one prime ideals in near-rings. It also develops properties of type one prime ideals, gives several examples illustrating where prime and type one prime are not equivalent, and investigates the properties of the type one prime radical. Several different types of conditions are given which guarantee that a prime ideal is type one. The class of all near-rings for which each prime ideal is type one is investigated and many examples of such near-rings are exhibited. Various localized distributivity conditions are found which are useful in establishing when prime ideals will be type one prime.     

INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type.First of all,we show that,if two finite-dimensional selfinjective k-algebras are sta...     

The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré-Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré-Liapunov method.     

Optimal replacement policy for obsolete components with general failure rates

Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old‐type components by the new‐type ones: either purely preventive, where all old‐type components are replaced as soon as the new‐type ones are available; either purely corrective, where the old‐type ones are replaced by new‐type ones only at failure; or a mixture of both strategies, where the old‐type ones are first replaced at failure by new‐type ones and next simultaneously preventively replaced after a fixed number of failed old‐type components. To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time. A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long‐time run. Numerical experiments conclude the paper. Copyright © 2008 John Wiley & Sons, Ltd.     

The kernels of vallee poussin type on P-adic fields

In this paper, we present a class of approximation identity operators of convolution type on the p-acid field K and on the ring of integersD⊂K, and study their approximation properties. All the kernels of these operators are of approximation identity, and are called de la Vallée Poussin type (VP type kernels). The structure of the VP type kernels onD is essentially an analogue of the classical one, however, the approximation properties are much better. Additionally, we discuss the maximal VP type operators and their properties. Supported by National Science Foundation of China     

New interpretations for noncrossing partitions of classical types

We interpret noncrossing partitions of type B and type D in terms of noncrossing partitions of type A. As an application, we get type-preserving bijections between noncrossing and nonnesting partitions of type B, type C and type D which are different from those in the recent work of Fink and Giraldo. We also define Catalan tableaux of type B and type D, and find bijections between them and noncrossing partitions of type B and type D respectively.     

Hypersurfaces whose mean curvature function is of finite type

We define finite mean type hypersurfaces to be hypersurfaces with mean curvature function of finite Chen-type. Then, we prove that hyperplanes are the only polynomial translation hypersurfaces of finite mean type in a Euclidean spaceE ⁿ⁺¹. And we show that the only non-conic hyperquadrics of finite mean type in Euclidean spaces are the hyperspheres and the cylinders on spheres. Finally, we state that, among all hypercylinders in a Euclidean spaceE ⁿ⁺¹, the only ones of finite mean type are those on finite mean type planar curves.     

Success runs of lengthk in Markov dependent trials

The geometric type and inverse Polýa-Eggenberger type distributions of waiting time for success runs of lengthk in two-state Markov dependent trials are derived by using the probability generating function method and the combinatorial method. The second is related to the minimal sufficient partition of the sample space. The first two moments of the geometric type distribution are obtained. Generalizations to ballot type probabilities of which negative binomial probabilities are special cases are considered. Since the probabilities do not form a proper distribution, a modification is introduced and new distributions of orderk for Markov dependent trials are developed.     

On the convergence of type I Hermite–Padé approximants

Padé approximation has two natural extensions to vector rational approximation through the so-called type I and type II Hermite–Padé approximants. The convergence properties of type II Hermite–Padé approximants have been studied. For such approximants Markov and Stieltjes type theorems are available. To the present, such results have not been obtained for type I approximants. In this paper, we provide Markov and Stieltjes type theorems on the convergence of type I Hermite–Padé approximants for Nikishin systems of functions.     

On sufficiency and duality in multiobjective programming problem under generalized <Emphasis Type="Italic">α</Emphasis>-type I univexity

In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized α-univex type I vector valued functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir type duality results are also presented.     

Split‐type octonion matrix

The split and hyperbolic (countercomplex) octonions are eight‐dimensional nonassociative algebras over the real numbers, which are in the form , where e_m's have different properties for them. The main purpose of this paper is to define the split‐type octonion and its matrix whose inputs are split‐type octonions and give some properties for them by using the real quaternions, split, and hyperbolic (countercomplex) octonions. On the other hand, to make some definitions, we present some operations on the split‐type octonions. Also, we show that every split‐type octonions can be represented by 2 × 2 real quaternion matrix and 4 × 4 complex number matrix. The information about the determinants of these matrix representations is also given. Besides, the main features of split‐type octonion matrix concept are given by using properties of  real quaternion matrices. Then, 8n × 8nreal matrix representations of split‐type octonion matrices are shown, and some algebraic structures are examined. Additionally, we introduce real quaternion adjoint matrices of split‐type octonion matrices. Moreover, necessary and sufficient conditions and definitions are given for split‐type octonion matrices to be special split‐type octonion matrices. We describe some special split‐type octonion matrices. Finally, oct‐determinant of split‐type octonion matrices is defined. Definitive and understandable examples of all definitions, theorems, and conclusions were given for a better understanding of all these concepts.     

Generalized Invexity and Duality in Multiobjective Programming Problems

In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond–Weir and general Mond–Weir type duality under the above generalized type I assumptions.     

Ando–Hiai type inequalities for multivariate operator means

ABSTRACT

We present several Ando–Hiai type inequalities for n-variable operator means for positive invertible operators. Ando–Hiai's inequalities given here are not only of the original type but also of the complementary type and of the reverse type involving the generalized Kantorovich constant.     

Generalized nonsmooth invexity over cones in vector optimization

In this paper K-nonsmooth quasi-invex and (strictly or strongly) K-nonsmooth pseudo-invex functions are defined. By utilizing these new concepts, the Fritz–John type and Kuhn–Tucker type necessary optimality conditions and number of sufficient optimality conditions are established for a nonsmooth vector optimization problem wherein Clarke’s generalized gradient is used. Further a Mond Weir type dual is associated and weak and strong duality results are obtained.     

On 𝒦-Nonsingular Modules and Applications

We introduce the notion of 𝒦-nonsingularity of a module and show that the class of 𝒦-nonsingular modules properly contains the classes of nonsingular modules and of polyform modules. A necessary and sufficient condition is provided to ensure that this property is preserved under direct sums. Connections of 𝒦-nonsingular modules to their endomorphism rings are investigated. Rings for which all modules are 𝒦-nonsingular are precisely determined. Applications include a type theory decomposition for 𝒦-nonsingular extending modules and internal characterizations for 𝒦-nonsingular continuous modules which are of type I, type II, and type III, respectively.     

Hyperbolic spaces are of strictly negative type

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.

     

Generalized Abel type integral equations with localized fractional integrals and derivatives

Generalized Abel type integral equations with Gauss, Kummer's and Humbert's confluent hypergeometric functions in the kernel and generalized Abel type integral equations with localized fractional integrals are considered. The left-hand sides of these equations are inversed by using generalized fractional derivatives. Explicit solutions of the equations in the class of locally summable functions are obtained. They are represented in terms of hypergeometric functions. Asymptotic power exponential type expansions of the generalized and localized fractional integrals are obtained. The base solutions of the generalized Abel type integral equation are given in the form of asymptotic series.     

Learning formation control for fractional‐order multiagent systems

In this paper, we use 2 iterative learning control schemes (P‐type and PI‐type) with an initial learning rule to achieve the formation control of linear fractional‐order multiagent systems. To realize the finite‐time consensus, we assume repeatable operation environments as well as a fixed but directed communication topology for the fractional‐order multiagent systems. Both P‐type and PI‐type update laws are applied to generate the control commands for each agent. It is strictly proved that all agents are driven to achieve an asymptotical consensus as the iteration number increases. Two examples are simulated to verify the effectiveness of the proposed algorithms.     

Quivers of finite mutation type and skew-symmetric matrices

Quivers of finite mutation type are certain directed graphs that first arised in Fomin-Zelevinsky’s theory of cluster algebras. It has been observed that these quivers are also closely related with different areas of mathematics. In fact, main examples of finite mutation type quivers are the quivers associated with triangulations of surfaces. In this paper, we study structural properties of finite mutation type quivers in relation with the corresponding skew-symmetric matrices. We obtain a characterization of finite mutation type quivers that are associated with triangulations of surfaces and give a new numerical invariant for their mutation classes.