Asymptotic Properties of Sums of Upper Records

Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold and Villaseñor (1999) are covered by our results.     

All-optical reconfigurable logic operations with the help of terahertz optical asymmetric demultiplexer

An all-optical reconfigurable logic operation essentially constitutes a key technology for avoiding complex and speed limited optoelectronics conversions and performing various processing tasks. All-optical reconfigurable logic operations with the help of terahertz optical asymmetric demultiplexer (TOAD) is proposed and described. The paper describes the all-optical reconfigurable logic operations using a set of all-optical multiplexer and optical switches. We have tried to exploit the advantages of TOAD-based switch to design an integrated all-optical circuit which can perform the different logic operations AND, XOR, NOR and NOT. Numerical simulation confirming described methods is given in this paper.     

Density functional investigation on the structures and properties of Li atom doped Au20 cluster

Structures and properties of an Au₂₀ cluster doped with two Li atoms, Au₁₈Li₂, have been investigated using relativistic density functional theory within the framework of the zeroth-order regular approximation. Various initial structures have been generated and employed for geometry optimization followed by vibration analysis to check the stability of the final optimized structures. We have calculated various properties like binding energy, ionization potential, electron affinity and the HOMO–LUMO gap of these structures. It has been found that two dopant Li atoms favour occupying two different surface positions of the pyramidal Au₂₀ cluster. The binding energy of the surface-doped Au₁₈Li₂ cluster is 1.017?eV higher than that of the pure Au₂₀ cluster and the HOMO–LUMO gap (1.742?eV) is as high as a pure Au₂₀ cluster (1.786?eV). Interestingly, we observe that the HOMO–LUMO gap as well as the binding energy can be increased beyond those of the Au₁₈Li₂ cluster with the help of further Li atom doping. In fact, a doped tetrahedral Au₁₆Li₄ cluster, where all the dopants are at the surface sites, possesses a very high HOMO–LUMO gap of 2.117?eV. Geometric and energetic parameters indicate that the Au₁₆Li₄ cluster might be considered as a possible ‘superatom’ in the design of novel cluster-assembled materials.     

Ontological Models,Preparation Contextuality and Nonlocality

The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some \(\psi \) -epistemic models without any use of Bell’s inequality. In particular, nonlocality of a non maximally \(\psi \) -epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger’s steerability of the maximally entangled state of two qubits (Leifer and Maroney, Phys Rev Lett 110:120401, 2013). In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality.     

All-optical prefix tree adder with the help of terahertz optical asymmetric demultiplexer

We propose and describe an all-optical prefix tree adder with the help of a terahertz optical asymmetric demultiplexer (TOAD) using a set of optical switches. The prefix tree adder is useful in compound adder implementation. It is preferred over the ripple carry adder and the carry lookahead adder. We also describe the principle and possibilities of the all-optical prefix tree adder. The theoretical model is presented and verified through numerical simulation. The new method promises higher processing speed and accuracy. The model can be extended for studying more complex all-optical circuits of enhanced functionality in which the prefix tree adder is the basic building block.     

All-optical adder/subtractor based on terahertz optical asymmetric demultiplexer

An all-optical adder/subtractor （A/S） unit with the （TOAD） is proposed. The all-optical A/S unit with help of terahertz optical asymmetric demultiplexer a set of all-optical full-adders and optical exclusive- ORs （XORs）, can be used to perform a fast central processor unit using optical hardware components. We try to exploit the advantages of TOAD-based optical switch to design an integrated all-optical circuit which can perform binary addition and subtraction. With computer simulation results confirming the described methods, conclusions are given.     

Convergence of tail sum for records

Suppose is the sequence of lower records from a distribution F, where F is continuous with . We derive conditions under which logarithm of the tail sum of records, ∑ _j=n ^∞ R _n ^(L) (F), properly centered and scaled, converge weakly. We also prove two results on Π-varying and regularly varying functions, which are of independent interest.     

Role of Ab Initio Calculations in the Design and Development of Organometallic Lanthanide‐Based Single‐Molecule Magnets

Single‐molecule magnets based on lanthanides are very attractive due to their potential applications proposed in the area of microelectronic devices. Very recent advances in this area are due to the blend of conventional lanthanide chemistry with organometallic ligands, and several breakthrough achievements are attained with this combination. Ab initio methods based on multi‐reference CASSCF calculations are playing a vital role in the design and development of such molecules. In this minireview, we aim to appraise various contributions in the area of organometallic lanthanide complexes (those containing lanthanide‐carbon bonds) and describe how these robust wavefunction‐based methods have played a constructive role not only in rationalizing the observed magnetic properties but also proven to be a potential predictive tool with some selected examples.     

Orientational correlation and velocity distributions in uniform shear flow of a dilute granular gas

Using particle simulations of the uniform shear flow of a rough dilute granular gas, we show that the translational and rotational velocities are strongly correlated in direction, but there is no orientational correlation-induced singularity at perfectly smooth (beta=-1) and rough (beta=1) limits for elastic collisions (e=1); both the translational and rotational velocity distribution functions remain close to a Gaussian for these two limiting cases. Away from these two limits, the orientational as well as spatial velocity correlations are responsible for the emergence of non-Gaussian high-velocity tails. The tails of both distribution functions follow stretched exponentials, with the exponents depending on normal (e) and tangential (beta) restitution coefficients.