In recent years, approximation algorithms based on randomized rounding of fractional optimal solutions have been applied to several classes of discrete optimization problems. In this paper, we describe a class of rounding methods that exploits the structure and geometry of the underlying problem to round fractional solution to 0–1 solution. This is achieved by introducing dependencies in the ro...

The problem of allocating indivisible objects arises in the allocation courses, spectrum licenses, landing slots at airports and assigning students to schools. We propose a technique for making such allocations that is based on rounding a fractional allocation. Under the assumption that no agent wants to consume more than k items, the rounding technique can be interpreted as giving agents lotte...

In this article, we study a system of Hilfer (k,ψ)-fractional differential equations, subject to nonlocal boundary conditions involving (k,ψ)-derivatives and (k,ψ)-integrals. The results for the mentioned are established by using Mönch’s fixed point theorem, then Ulam–Hyers technique is used verify stability solution proposed system. general, symmetry fractional equations related each other. Wh...

This work is devoted to the study of solutions around an α-singular point x0 ∈ [a, b] for linear fractional differential equations of the form [Lnα(y)](x) = g(x, α), where [Lnα(y)](x) = y(nα)(x)+ n−1 ∑ k=0 ak(x)y (kα)(x) with α ∈ (0, 1]. Here n ∈ N , the real functions g(x) and ak(x) (k = 0, 1, . . . , n−1) are defined on the interval [a, b], and y(nα)(x) represents sequential fractional deriva...

In computer networks, toughness is an important parameter which is used to measure the vulnerability of the network. Zhou et al. [24] obtains a toughness condition for a graph to be fractional (k,m)–deleted and presents an example to show the sharpness of the toughness bound. In this paper we remark that the previous example does not work and inspired by this fact, we present a new toughness co...

We find the solution of the sl(3) k singular vector decoupling equations on 3–point functions for the particular case when one of the fields is of weight w 0 · kΛ 0. The result is a function with non-trivial singularities in the flag variables, namely a linear combination of 2 F 1 hypergeometric functions. This calculation fills in a gap in [1] and confirms the sl(3) k fusion rules determined t...

We study the branching program complexity of the tree evaluation problem, introduced in [BCM+09a] as a candidate for separating NL from LogCFL. The input to the problem is a rooted, balanced dary tree of height h, whose internal nodes are labelled with d-ary functions on [k] = {1, . . . , k}, and whose leaves are labelled with elements of [k]. Each node obtains a value in [k] equal to its d-ary...

nezam-abad area is located in southwest of shazand (arak) which is a part of sanandaj-sirjan zone. major intrusive rocks of nezam-abad are quartz diorite and minor amount of granodiorite. leucogranitic, pegmatite dykes and quartz-tourmaline veins were intruded the quartz diorite. quartz diorites are mainly composed of plagioclase, hornblende, biotite, quartz and pyroxene as major minerals. majo...