A further result on the oscillation of delay difference equations

AbstractIn this paper, we are concerned with the delay difference equations of the form∗yn+1 − yn + pnyn−k = 0, n = 0, 1, 2, …, (∗)where pn ≥ 0 and k is a positive integer. We prove by using a new technique that∑n=0∞ ∑i=nn+kpi ln ∑i=nn+k pi + 1 − sign ∑i=nn+k pi − ∑i=n+1n+k pi ln ∑i=n+1n+k pi + 1 − sign ∑i=n+1n+k pi = ∞guarantees that all solutions of equation (∗) oscillate, which improves many previous well-known results. In particular, our theorems also fit the case where Σn−1i=n−kpi ≤ kk+1(k + 1)k+1. In addition, we present a nonoscillation sufficient condition for equation (∗)

N-qubit entanglement via the Jy2J_y^2-type collective interaction

We investigate quantum correlations of the $N$-qubit states via a collective pseudo-spin interaction ($\propto J_y^2$) on arbitrary pure separable states for a given interval of time. Based on this dynamical generation of the $N$-qubit maximal entangled states, a quantum secret sharing protocol with $N$ continuous classical secrets is developed.Comment: 12 pages, 3 figure

Study protocol for a non-inferiority randomised controlled trial of SKY breathing meditation versus cognitive processing therapy for PTSD among veterans

Introduction Post-traumatic stress disorder (PTSD) is a debilitating, highly prevalent condition. Current clinical practice guidelines recommend trauma-focused psychotherapy (eg, cognitive processing therapy; CPT) as the first-line treatment for PTSD. However, while these treatments show clinically meaningful symptom improvement, the majority of those who begin treatment retain a diagnosis of PTSD post-treatment. Perhaps for this reason, many individuals with PTSD have sought more holistic, mind–body, complementary and integrative health (CIH) interventions. However, there remains a paucity of high-quality, active controlled efficacy studies of CIH interventions for PTSD, which precludes their formal recommendation. Methods and analyses We present the protocol for an ongoing non-inferiority parallel group randomised controlled trial (RCT) comparing the efficacy of a breathing meditation intervention (Sudarshan Kriya Yoga [SKY]) to a recommended evidence-based psychotherapy (CPT) for PTSD among veterans. Assessors are blinded to treatment group. The primary outcome measure is the PTSD Checklist-Civilian Version and a combination of clinical, self-report, experimental and physiological outcome measures assess treatment-related changes across each of the four PTSD symptom clusters (re-experiencing, avoidance, negative cognitions or mood and hyperarousal/reactivity). Once the RCT is completed, analyses will use both an intent-to-treat (using the ‘last observation carried forward’ for missing data) and a per-protocol or ‘treatment completers’ procedure, which is the most rigorous approach to non-inferiority designs. Ethics and dissemination To the best of our knowledge, this is this first non-inferiority RCT of SKY versus CPT for PTSD among veterans. The protocol is approved by the Stanford University Institutional Review Board. All participants provided written informed consent prior to participation. Results from this RCT will inform future studies including larger multi-site efficacy RCTs of SKY for PTSD and other mental health conditions, as well as exploration of cost-effectiveness and evaluation of implementation issues. Results will also inform evidence-based formal recommendations regarding CIH interventions for PTSD

Guide to verification and validation of the SCALE-4 radiation shielding software

Whenever a decision is made to newly install the SCALE radiation shielding software on a computer system, the user should run a set of verification and validation (V&V) test cases to demonstrate that the software is properly installed and functioning correctly. This report is intended to serve as a guide for this V&V in that it specifies test cases to run and gives expected results. The report describes the V&V that has been performed for the radiation shielding software in a version of SCALE-4. This report provides documentation of sample problems which are recommended for use in the V&V of the SCALE-4 system for all releases. The results reported in this document are from the SCALE-4.2P version which was run on an IBM RS/6000 work-station. These results verify that the SCALE-4 radiation shielding software has been correctly installed and is functioning properly. A set of problems for use by other shielding codes (e.g., MCNP, TWOTRAN, MORSE) performing similar V&V are discussed. A validation has been performed for XSDRNPM and MORSE-SGC6 utilizing SASI and SAS4 shielding sequences and the SCALE 27-18 group (27N-18COUPLE) cross-section library for typical nuclear reactor spent fuel sources and a variety of transport package geometries. The experimental models used for the validation were taken from two previous applications of the SASI and SAS4 methods

Non-Markovian dynamics for an open two-level system without rotating wave approximation: Indivisibility versus backflow of information

By use of the two measures presented recently, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and the reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relations between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed

Efficient Conditional Proxy Re-encryption with Chosen-Ciphertext Security

Recently, a variant of proxy re-encryption, named conditional proxy re-encryption (C-PRE), has been introduced. Compared with traditional proxy re-encryption, C-PRE enables the delegator to implement fine-grained delegation of decryption rights, and thus is more useful in many applications. In this paper, based on a careful observation on the existing definitions and security notions for C-PRE, we reformalize more rigorous definition and security notions for C-PRE. We further propose a more efficient C-PRE scheme, and prove its chosenciphertext security under the decisional bilinear Diffie-Hellman (DBDH) assumption in the random oracle model. In addition, we point out that a recent C-PRE scheme fails to achieve the chosen-ciphertext security

Induced four fold anisotropy and bias in compensated NiFe/FeMn double layers

A vector spin model is used to show how frustrations within a multisublattice antiferromagnet such as FeMn can lead to four-fold magnetic anisotropies acting on an exchange coupled ferromagnetic film. Possibilities for the existence of exchange bias are examined and shown to exist for the case of weak chemical disorder at the interface in an otherwise perfect structure. A sensitive dependence on interlayer exchange is found for anisotropies acting on the ferromagnet through the exchange coupling, and we show that a wide range of anisotropies can appear even for a perfect crystalline structure with an ideally flat interface.Comment: 7 pages, 7 figure

Generalized Transformation for Decorated Spin Models

The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes $[-s,s]$ is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising models. We apply this transformation to a particular mixed spin-(1/2,1) and (1/2,2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-$S$ square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also include combinations of three-body and four-body interactions, particularly we considered spin 1 and 2.Comment: 16 pages, 4 figure

Statistical mechanics of RNA folding: importance of alphabet size

We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.Comment: 7 figures; uses revtex

Potential benefits and impacts on the CRWMS transportation system of filling spent fuel shipping casks with depleted uranium silicate glass

A new technology, the Depleted Uranium Silicate COntainer Fill System (DUSCOFS), is proposed to improve the performance and reduce the uncertainties of geological disposal of spent nuclear fuel (SNF), thus reducing both radionuclide release rates from the waste package and the potential for repository nuclear criticality events. DUSCOFS may also provide benefits for SNF storage and transport if it is loaded into the container early in the waste management cycle. Assessments have been made of the benefits to be derived by placing depleted uranium silicate (DUS) glass into SNF containers for enhancing repository performance assessment and controlling criticality over geologic times in the repository. Also, the performance, benefits, and impacts which can be derived if the SNF is loaded into a multi-purpose canister with DUS glass at a reactor site have been assessed. The DUSCOFS concept and the benefits to the waste management cycle of implementing DUSCOFS early in the cycle are discussed in this paper