Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation

In this paper, the traditional inventory lot-size model is extended to allow not only for general partial backlogging rate but also for inflation. The assumptions of equal cycle length and constant shortage length imposed in the model developed by Moon et al. [Moon, I., Giri, B.C., Ko, B., 2005. Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting, European Journal of Operational Research 162(3), 773–785] are also relaxed. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule is proved and further the convexity of the total cost function of the inventory system in the number of replenishments is established. The theoretical results here amend those in Yang et al. [Yang, H.L., Teng, J.T., Chern, M.S., 2001. Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand, Naval Research Logistics 48(2), 144–158] and provide the solution to those two counterexamples by Skouri and Papachristos [Skouri, K., Papachristos, S., 2002. Note on “deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand” by Yang et al. Naval Research Logistics 49(5), 527–529.]. Finally we propose an algorithm to find the solution, and obtain some managerial results by using sensitivity analyses.     

Global Existence for Semilinear Evolution Equations with Nonlocal Conditions

In this paper, we study the global existence of solutions for semilinear evolution equations with nonlocal conditions, via a fixed point analysis approach. Using the Leray–Schauder Alternative, we derive conditions under which a solution exists globally.     

Monotonic solutions of a perturbed quadratic fractional integral equation

We present an existence theorem for monotonic solutions of a perturbed quadratic fractional integral equation in C[0,1]. The concept of a measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. Finally, we give an example for indicating the natural realizations of our abstract result presented in the paper.     

A STUDY OF A FULLY COUPLED TWO-PARAMETER SYSTEM OF SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL INTEGRO-MULTIPOINT BOUNDARY CONDITIONS

In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.     

Fractional Differential Equations with Nonlocal Integral and Integer–Fractional-Order Neumann Type Boundary Conditions

We introduce a new concept of the coupling of nonlocal integral and integer–fractional-order Neumann type boundary conditions, and discuss the existence and uniqueness of solutions for a coupled system of fractional differential equations supplemented with these conditions. The existence of solutions is derived from Leray–Schauder’s alternative and Schauder’s fixed point theorem, while the uniqueness of solutions is established by means of Banach’s contraction mapping principle. The results obtained in this paper are well illustrated with the aid of examples.     

The bend angle of water in ice Ih and liquid water: The significance of implementing the nonlinear monomer dipole moment surface in classical interaction potentials

The implementation of the physically accurate nonlinear dipole moment surface of the water monomer in the context of the Thole-type, polarizable, flexible interaction potential results in the only classical potential, which, starting from the gas phase value for the bend angle (104.52 degrees), reproduces its experimentally observed increase in the ice Ih lattice and in liquid water. This is in contrast to all other classical potentials to date, which predict a decrease of the monomer bend angle in ice Ih and in liquid water with respect to the gas phase monomer value. Simulations under periodic boundary conditions of several supercells consisting of up to 288 molecules of water used to sample the proton disorder in the ice Ih lattice yield an average value of vartheta(HOH)(I(h))=108.4 degrees +/-0.2 degrees for the minimized structures (T=0 K) and 108.1 degrees +/-2.8 degrees at T=100 K. Analogous simulations for liquid water predict an average value of vartheta(HOH)(liquid)=106.3 degrees +/-4.9 degrees at T=300 K. The increase of the monomer bend angle of water in condensed environments is attributed to the use of geometry-dependent charges that are used to describe the nonlinear character of the monomer's dipole moment surface. Our results suggest a new paradigm in the development of classical interaction potential models of water that can be used to describe condensed aqueous environments.     

Electrical conductance study of theta-liquid bridges

This work investigates the behavior of small liquid bridges that are formed between two horizontal supporting surfaces, aligned at the vertical direction. The contact lines of the liquid bridges are not edge-pinned but free to move across the supporting surfaces with the contact angle as a parameter (theta-bridges). An a.c. electrical conductance technique coupled with high resolution optical images is used to characterize the geometrical details of constant volume liquid bridges when their length is increased gradually until rupture. A mathematical framework is developed for the identification of the geometrical characteristics of theta-liquid bridges explicitly from conductance data. Theoretical predictions show good agreement with measurements for most of the bridge lengths (separation distance between supports) except close to the rupture point where the bridge is highly stretched. It is further shown that for short and moderate separation distances the present model can be used with confidence to determine the bridge volume and neck radius from the electrical signal.     

Existence Results for Semilinear Perturbed Functional Differential Equations of Neutral Type with Infinite Delay

In this paper, by using semigroup theory and a nonlinear alternative for the sum of a completely continuous and a contraction operator, we establish sufficient conditions for the existence of solutions for perturbed semilinear neutral functional differential equations with infinite delay.