At the planar interface between a material and vacuum, complex surface response S ( ω stretchy="false">) = stretchy="false">[ ε <mm...

We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in [0, 1]. Similar notions have been considered for kernels; we extend them to more general types of ranges. We then consider approximations of these range spaces through ε-nets and εsamples (aka ε-approximations). We characterize when size ...

There are many chemical molecules whose names are Cannabigerol (CBG), cannabidol (CBD), cannabichromene (CBC), tetrahydrocannabivarin (THCV), cannabigerovarinic acid (CBGV) and cannabidiolic acid (CBDA) derived from Marijuana. Theoretical methods were used to compare the chemical and biological activities of the six major molecules. Molecules were compared with their chemical activities using m...

We view some ideas for improvement, extension and application of proximal point methods and the auxiliary problem principle to variational inequalities in Hilbert spaces. These methods are closely related and will be joined in a general framework, which admits a consecutive approximation of the problem data including applications of finite element techniques and the ε-enlargement of monotone op...

Let ε > 0 and consider ε2u′′(t; ε) + u′(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε)ds+ f(t; ε), t ≥ 0, u(0; ε) = u0(ε), u ′(0; ε) = u1(ε), and w′(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t), t ≥ 0, w(0) = w0, in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear operator for t ≥ 0. With some conv...

It has long been known, since the classical work of (Arora, Karger, Karpinski, JCSS 99), that Max-CUT admits a PTAS on dense graphs, and more generally, Max-k-CSP admits a PTAS on “dense” instances with Ω(n) constraints. In this paper we extend and generalize their exhaustive sampling approach, presenting a framework for (1−ε)-approximating any Max-k-CSP problem in sub-exponential time while si...

We use class field theory, specifically Drinfeld modules of rank 1, to construct a family of asymptotically good algebraic-geometric (AG) codes over fixed alphabets. Over a field of size l, these codes are within 2/( √ l − 1) of the Singleton bound. The functions fields underlying these codes are subfields with a cyclic Galois group of the narrow ray class field of certain function fields. The ...

criticism of public extension services has resulted in various countries seeking alternative approaches for provision of these services. in all these approaches, extension personnel are the key factors to the success of the implementation. today, agricultural extension services in turkey bear the responsibility of the ministry of food, agriculture and livestock. a number of non-public extension...