A class of B-(p,r)-invex functions and mathematical programming

Invexity of a function is generalized. The new class of nonconvex functions, called B-(p,r)-invex functions with respect to η and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(p,r)-invex functions with respect to η and b are studied. Further, mathematical programming problems involving B-(p,r)-invex functions with respect to η and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems.     

CTL AgentSpeak(L): A specification language for agent programs

This work introduces CTL AgentSpeak(L), a logic to specify and verify expected properties of rational agents implemented in the well-known agent oriented programming language AgentSpeak(L). Our approach is closely related to the BDICTL multi-modal logic, used to reason about agents in terms of their beliefs (B), desires (D), intentions (I), and the temporal logic CTL. A new interpretation for the temporal operators, grounded in the transition system induced by the operational semantics of AgentSpeak(L), is proposed. The main contribution of the approach is a better understanding of the relation between the programming language and its logical specification, enabling us to prove expected or desired properties for any agent programmed in the language, e.g., commitment strategies. The results, as well as the specification language proposed, are very useful to reconcile computational and philosophical aspects of practical reasoning, e.g., approaching single-minded commitment as a policy-based reconsideration case.     

Weak barrelledness for C(X) spaces

Buchwalter and Schmets reconciled C_c(X) and C_p(X) spaces with most of the weak barrelledness conditions of 1973, but could not determine if -barrelled ⇔ ?^∞-barrelled for C_c(X). The areas grew apart. Full reconciliation with the fourteen conditions adopted by Saxon and Sánchez Ruiz needs their 1997 characterization of Ruess' property (L), which allows us to reduce the C_c(X) problem to its 1973 status and solve it by carefully translating the topology of Kunen (1980) and van Mill (1982) to find the example that eluded Buchwalter and Schmets. The more tractable C_p(X) readily partitions the conditions into just two equivalence classes, the same as for metrizable locally convex spaces, instead of the five required for C_c(X) spaces. Our paper elicits others, soon to appear, that analytically characterize when the Tychonov space X is pseudocompact, or Warner bounded, or when C_c(X) is a df-space (Jarchow's 1981 question).     

Polynomial sequential continuity on C(K,E) spaces

We show that, for bounded sequences in C(K,E), the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence. We introduce several conditions on E under which different versions of the result are true when K is a scattered compact space. These conditions are related with some others appeared in the literature and they seem to be of independent interest.     

A note on the extension of BV functions in metric measure spaces

In this note, a classical extension result for BV functions due to Yu.D. Burago and V.G. Maz'ja [Yu.D. Burago, V.G. Maz'ja, Potential Theory and Function Theory for Irregular Regions, Seminars in Math., vol. 3, V.A. Steklov Math. Inst., Leningrad, 1969 (translated from Russian)] is generalized to the abstract setting of doubling metric measure spaces endowed with a differentiation structure called D-structure.     

On properties of discrete (r, q) and (s, T) inventory systems

We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L^?-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties established previously using continuous variables invalid. We revise these properties in the discrete space.     

On the GI/M/1/N queue with multiple working vacations—analytic analysis and computation

We consider finite buffer single server GI/M/1 queue with exhaustive service discipline and multiple working vacations. Service times during a service period, service times during a vacation period and vacation times are exponentially distributed random variables. System size distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system etc. have been obtained. The model has potential application in the area of communication network, computer systems etc. where a single channel is allotted for more than one source.     

Analysis of an M/G/∞ queue with batch arrivals and batch-dedicated servers

We analyze an M/G/∞ queue with batch arrivals, where jobs belonging to a batch have to be processed by the same server. The number of jobs in the system is characterized as a compound Poisson random variable through a scaling of the original arrival and batch size processes.     

A new method of solving nonlinear mathematical programming problems involving r-invex functions

A new approach to a solution of a nonlinear constrained mathematical programming problem involving r-invex functions with respect to the same function η is introduced. An η-approximated problem associated with an original nonlinear mathematical programming problem is presented that involves η-approximated functions constituting the original problem. The equivalence between optima points for the original mathematical programming problem and its η-approximated optimization problem is established under r-invexity assumption.     

Eigenvalues of p(x)-Laplacian Dirichlet problem

This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem

     

Composition operators from F(p, q, s) spaces to the nth weighted-type spaces on the unit disc

In this note we characterize the boundedness and compactness of the composition operator from the general function space F(p, q, s) to the nth weighted-type space on the unit disk, where the nth weighted-type space has been recently introduced by Stevo Stevi?.     

A novel use of t-packings to construct d-disjunct matrices

A t-packing is an ordered pair (V,P) where V is a v-set and P is a collection of k-subsets (blocks) of V such that each t-subset of V occurs in at most one block of P. If each t-subset of V occurs in exactly one block of P, then (V,P) is known as a Steiner (t,k,v)-design. In this paper, we explore a novel use of t-packings to construct d-disjunct matrices.     

Combined m-consecutive and k-out-of-n sliding window systems

This paper proposes a new model that generalizes the linear multi-state sliding window system. In this model the system consists of n linearly ordered multi-state elements. Each element can have different states: from complete failure up to perfect functioning. A performance rate is associated with each state. The system fails if at least one of the following two conditions is met: (1) there exist at least m consecutive overlapping groups of r adjacent elements having the cumulative performance lower than V; (2) there exist at least k arbitrarily located groups of r adjacent elements having the cumulative performance lower than W. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of evaluating system reliability and elements’ reliability importance indices are presented. Optimal sequencing of system elements is demonstrated.     

Generalized composition operators from F(p, q, s) spaces to Bloch-type spaces

Let H(B) denote the space of all holomorphic functions on the unit ball B of Cⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. In this paper, we investigate the boundedness and compactness of the generalized composition operator

     

Fluid model driven by an M/G/1 queue with multiple exponential vacations

This paper studies a fluid model driven by an M/G/1 queue with multiple exponential vacations. By introducing various vacation strategies to the fluid model, we can provide greater flexibility for the design and control of input rate and output rate. The Laplace transform of the steady-state distribution of the buffer content is expressed through the minimal positive solution to a crucial equation. Then the performance measure-mean buffer content, which is independent of the vacation parameter, is obtained. Finally, with some numerical examples, the parameter effect on the mean buffer content is presented.     

Reliability of a consecutive (r, s)-out-of-(m, n):F lattice system with conditions on the number of failed components in the system

A consecutive(r, s)-out-of-(m, n):F lattice system which is defined as a two-dimensional version of a consecutive k-out-of-n:F system is used as a reliability evaluation model for a sensor system, an X-ray diagnostic system, a pattern search system, etc. This system consists of m × n components arranged like an (m, n) matrix and fails iff the system has an (r, s) submatrix that contains all failed components. In this paper we deal a combined model of a k-out-of-mn:F and a consecutive (r, s)-out-of-(m, n):F lattice system. Namely, the system has one more condition of system down, that is the total number of failed components, in addition to that of a consecutive (r, s)-out-of-(m, n):F lattice system. We present a method to obtain reliability of the system. The proposed method obtains the reliability by using a combinatorial equation that does not depend on the system size. Some numerical examples are presented to show the relationship between component reliability and system reliability.     

Algorithmic analysis of the Geo/Geo/c retrial queue

In this paper, we consider a discrete-time queue of Geo/Geo/c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/M/c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis.     

Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions

A system with n independent components which has a k-out-of-n: G structure operates if at least k components operate. Parallel systems are 1-out-of-n: G systems, that is, the system goes out of service when all of its components fail. This paper investigates the mean residual life function of systems with independent and nonidentically distributed components. Some examples related to some lifetime distribution functions are given. We present a numerical example for evaluating the relationship between the mean residual life of the k-out-of-n: G system and that of its components.     

Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons

A discrete k-out-of-n: G system with multi-state components is modelled by means of block-structured Markov chains. An indefinite number of repairpersons are assumed and PH distributions for the lifetime of the units and for the repair time are considered. The units can undergo two types of failures, repairable or non-repairable. The repairability of the failure can depend on the time elapsed up to failure. The system is modelled and the stationary distribution is built by using matrix analytic methods. Several performance measures of interest, such as the conditional probability of failure for the units and for the system, are built into the transient and stationary regimes. Rewards are included in the model. All results are shown in a matrix algorithmic form and are implemented computationally with Matlab. A numerical example of an optimization problem shows the versatility of the model.