Lowest Upper Bound Research Articles

Physical mechanism of AdS instability and universality of holographic thermalization

Gravitational falling in the Anti-deSitter Spacetime (AdS) has two characteristic properties: i) A thick shell becomes a thin shell. ii) Any shape become spherical. Such a focusing character of the AdS space, for collapse of dust clouds, leads to the rapid thermalization mechanism in strongly interacting system. For a conformally flat boundary, we show that such focusing mechanism is universal in all known background geometries of D-branes as well as in those of AdS spacetime. We calculate the time scale for thermalization in terms of the total mass density and the lowest upper bound of the energy distribution of the initial particles. We find tth ~ (1 − c1/E2)1/2/T, which is less than the typical collision time so that softer modes thermalize first. We also suggest that the same idea can shed light on the collapse of waves belonging the heavy numerical relativity.

16-QAM Golay Complementary Sequence Sets with Arbitrary Lengths

In an orthogonal frequency division multiplexing (OFDM) communication system, the reduction of peak-to-mean envelope power ratio (PMEPR) is one of crucial issues. It is all known that in an OFDM system, Golay complementary sequence (CS) pairs result in lowest upper bound 2 of PMEPR. Hence, this letter focuses on constructions of 16-QAM Golay CS sets. The proposed two constructions can produce the required sequences with arbitrary lengths, including lots of unknown ones in the existing references, if there exist the quaternary Golay CS sets of such lengths, and the PMEPRs of the Golay CS pairs from both are at most 2. As a consequence, the resultant sequences by this letter can be used as the inputs of using non-radix-2 inverse fast Fourier transform (IFFT) in the time domain OFDM signals.

First order LUB approximations: characterization and algorithms

One of the major approaches to approximation of logical theories is the upper and lower bounds approach introduced by Selman and Kautz (1991, 1996). In this paper, we address the problem of lowest upper bound (LUB) approximation in a general setting. We characterize LUB approximations for arbitrary target languages, both propositional and first order, and describe algorithms of varying generality and efficiency for all target languages, proving their correctness. We also examine some aspects of the computational complexity of the algorithms, both propositional and first order; show that they can be used to characterize properties of whole families of resolution procedures; discuss the quality of approximations; and relate LUB approximations to other approaches existing in the literature which are not typically seen in the approximation framework, and which go beyond the “knowledge compilation” perspective that led to the introduction of LUBs.

On the image of an L-fuzzy group

In this short communication we show that if any subset of a lattice L containing its lowest upper bound is an image of an L-fuzzy group, then L must be a chain.

Thermodynamic approach to transport scalings in tokamaks

The cross-field plasma diffusion coefficient is expressed in terms of the perturbed potential energy W by making use of the nonlinearity of orbit diffusion. The thermodynamic bound of the energy W for a current-carrying collisionless plasma has been determined consistently with four constraints: the invariance of averaged Hamiltonian, angular momentum, entropy and density. It is found that with momentum invariance the major contribution from the plasma current cancels, and the lowest upper bound of W is determined by the high-order toroidal effect coupled with the plasma current, which yields the neo-Alcator (TFTR) scaling for the energy confinement time. When neoclassical deformation is allowed in the plasma distribution, the thermodynamic bound has additional terms which come from the neoclassical source of free energy due to the bootstrap current. When the poloidal beta is larger than a certain critical value, the energy confinement time shows the effect of density saturation, and becomes proportional to the plasma current.

On orthomodular amalgamations of Boolean algebras

I t is well known [1], [2] t h a t o r thomodular lattices and complete by or thomodular posers are completely determined by their Boolean sublattices and the way they are glued together. An analoguous result for Boolean orthoposets has been obtained by C. Lapifiska [3]. I n the present paper we intend to generalize these results to a rb i t ra ry or thomodular posers showing t h a t any such poser can be constructed in a canonical manner out of its Boolean sublattices. The construct ion is then used to prove t h a t any a rb i t ra ry poser can be embeded in an or thomodular poset, where embeding means an inj eetive mapping of posers respeeting arb i t rary meets and joins. :For a bijective embeding we shall use the not ion isomorphism. The greatest lower bound and lowest upper bound of elements in a poser are denoted by A and v respectively. An or thoeomplementa t ion of a poser L with greatest element I and lowesg element q) is a bijeetion N : L > L sueh t h a t a ' + N a exists for each a e L and (i) N N a = a, (ii) a --< b implies N b <= N a for a, b e L , (iii) N a v a -=I hold true. Dealing with several posers at a t ime we indicate the different operat ions and order relations in the different posers by a subindex i. A poser L together with an orthoeomplementat ion N is called an orthoposet . An or thoposet L is called a Boolean or thoposet iff addi t ional ly holds (1) for a l l a , b c L a ~ N b if and only if there exists a e e L with c-----avb. (2) for alla, b e L a G N b i f f a a b : ~ b .

Upper bounds of best one-sided approximations of the classes WrLΨ in the metric of L

The lowest upper bound is obtained for best one-sided approximations of classes (r=1,2 ...) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space L, where WrLΨ={f:f(x+2π)=f(x), f(r−1)(x) is absolutely continuous, ∥f(r)∥LΨ⩽1} and LΨ is an Orlicz space.