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A new general multistep predictor-corrector (PC) pair form is introduced for the numerical integration of second-order initial-value problems. Using this form, a new symmetric eight-step predictor-corrector method with minimal phase-lag and algebraic order ten is also constructed. The new method is based on the multistep symmetric method of Quinlan–Tremaine,¹ with eight steps and 8th algebraic order and is constructed to solve numerically the radial time-independent Schrödinger equation. It can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with minimal phase-lag is the most efficient of all the compared methods and for all the problems solved.

In this paper, we propose a symmetric alternating method of multipliers for minimizing the sum of two nonconvex functions with linear constraints, which contains the classic alternating direction method of multipliers in the algorithm framework. Based on the powerful Kurdyka–Łojasiewicz property, and under some assumptions about the penalty parameter and objective function, we prove that each bounded sequence generated by the proposed method globally converges to a critical point of the augmented Lagrangian function associated with the given problem. Moreover, we report some preliminary numerical results on solving $l_{1/2}$ regularized sparsity optimization and nonconvex feasibility problems to indicate the feasibility and effectiveness of the proposed method.

In this paper, two three-party cyclic teleportation schemes for real arbitrary quantum states of a single particle and two particles are proposed for the first time. In the first ($1\sim 2\sim 1$) scheme, Alice sends any single particle state to Bob, Bob sends any two-particle states to Charlie, and meanwhile Charlie sends any single particle state to Alice. In the second ($2\sim 2\sim 1$) scheme, with the help of the controller David, Alice sends any two-particle states to Bob, Bob sends any two-particle states to Charlie, and Charlie sends any single particle state to Alice simultaneously. Based on the maximum entangled quantum channel shared in advance, the communication participants carry out some Bell state measurement (BSM) measurements and carry out corresponding unitary transformation according to the results published by each other. After that, the cyclic teleportation of predetermined quantum information can be successfully realized. The success probability of teleportation of both schemes can reach 100%. Finally, this paper briefly analyzes the security of the two schemes and compares them with some previously published schemes from the perspective of inherent efficiency. The results show that the two schemes proposed in this paper are safe and have high inherent efficiency. Different from the previous symmetric cyclic quantum teleportation methods, the asymmetric cyclic quantum teleportation schemes proposed in this paper are more universal.

Frequency dividers are used in frequency synthesizers to generate specific frequencies or clock (CK) waveforms. As consequences of their operating principles, frequency dividers often produce output waveforms that exhibit duty cycles other than 50%. However, some circuits and systems, including dynamic memory systems and data converters, which accommodate frequency divider outputs, may need symmetric or 50%-duty-cycle clock waveforms to optimize timing margins or to obtain sufficient timing reliability. In this review paper, design principles and methods are studied to produce symmetric waveforms for the in-phase (I) and quadrature (Q) outputs of high-speed CMOS frequency dividers with design considerations from the logic gate level down to the transistor level in terms of speed, reliability, noise, and latency. A compact and robust multi-gigahertz frequency divider with moduli 12, 14, and 16 to provide I and Q outputs with 50% duty cycle is proposed and designed using a 90-nm digital CMOS process technology with 1.2-V supply.

In this paper, a new structure for multilevel converter based on improved H-bridge converter is presented. The proposed topology is a symmetric topology since the values of all voltage sources are equal. The proposed symmetric structure is a general topology which can be extended for any number of voltage levels at output voltage waveform to obtain the least value of total harmonic distortion (THD). Reduction of switching losses, conduction losses, the number of on-state switches in the current path, utilized DC voltage sources, and gate driver circuits are the main advantages of proposed symmetric structures in comparison with other symmetric topologies. All mathematical analysis on the proposed structure is presented in terms of power losses and maximum blocked voltage by switches. The comparison results with other recently presented symmetric topologies and traditional multilevel converter structures are provided. Experimental results for a thirteen-level converter based on presented structure are provided to validate the practicality of the suggested multilevel structure.

Multilevel inverter (MLI) has become more popular in high power, high voltage industries owing to its high quality output voltage waveform. This paper proposes a novel single phase extendable type MLI topology. The term ‘extendable’ is included since the presented topology can be extended with maximum number of dc voltage sources to synthesize larger output levels. This topology can be operated in both symmetrical and asymmetrical conditions. The major advantages of the proposed inverter topology include minimum switching components, reduced gate driver circuits, less harmonic distortion and reduced switching losses. The comparative analysis based on the number of switches, dc voltage sources and conduction switches between the proposed topology and other existing topologies is presented in this paper. The comparison results show that the proposed inverter topology requires fewer components. The performance of the proposed MLI topology has been analyzed in both symmetrical and asymmetrical conditions. The simulation model is developed using MATLAB/SIMULINK software to verify the performance of the proposed inverter topology and also the feasibility of the presented topology during the symmetrical condition has been validated experimentally.

Storage of data security has emerged as a basic necessity for both large- and small-scale industries. Cloud computing is internet-based computing technology in which people can work with their application with a high level of security in Internet of Things (IoT) enhanced devices. Cloud computing also provides privilege to store data that are collected from the devices in server side. Confidentiality and integrity of data play a major issue in cloud computing while preserving the IoT data. In this paper, the security of data is achieved by performing clustering and further applying cryptographic technique to the clustered data gathered from the devices that connected to the internet. Security of data can be improved by using a prominent cryptographic technique Attribute Based Encryption (ABE). Initially, the documents are clustered using the EM algorithm and clustered results are stored in various parts of the cloud. These documents are secured and can be accessed by the user who satisfies the attributes. In some cases, if the users’ attributes are not satisfied with the documents, it cannot be accessed by the corresponding user. Thus, the data from various devices are encrypted and maintained by the owner securely.

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

We make the study of the relationship between symmetrical coupling of coupling qubits and non-Markovian relaxation characteristics by utilizing concurrence. The results show that the relaxation characteristics of quantum system strongly depend on the coupling way between qubits and environment and the decoherence-free subspace may form under certain conditions. We find that when the system is initially at state or the mixed state generated by this state, we can make the quantum system always at the entangled state without entanglement sudden death (ESD) phenomenon by regulating the coupling between qubits and environment at complete anti-symmetric state. In contrast, when the system is initially at state or the mixed state generated by this state, then we must regulate the coupling way between qubits and environment at complete symmetric state to make the quantum system maintain at the entanglement state.

Given two numerical semigroups S and S', the distance between S and S' is the cardinality of S\S' plus the cardinality of S'\S. In this paper we study those numerical semigroups S for which there is a symmetric numerical semigroup whose distance to S is one.

Given a symmetric tensor on a real vector bundle of dimension two, we construct a space where this tensor corresponds to a scalar function. We prove that under certain regularity conditions such a space and the corresponding scalar function are smooth. We study the topology of this space for the case of surfaces and produce a version of Morse inequalities for symmetric tensors. We apply our results to the geometry of surfaces.

For a finite commutative ring R and a positive integer k, let G(R, k) denote the digraph whose set of vertices is R and for which there is a directed edge from a to a^k. The digraph G(R, k) is called symmetric of order M if its set of connected components can be partitioned into subsets of size M with each subset containing M isomorphic components. We primarily aim to factor G(R, k) into the product of its subdigraphs. If the characteristic of R is a prime p, we obtain several sufficient conditions for G(R, k) to be symmetric of order M.

Understanding currency fluctuations carries a high level of risk. A currency can slide or spike as a response of an economic indicators revelation or an unexpected political event, both of which are unforeseeable. As foreign investors become more optimistic about the country’s future, a healthier economy usually requires a strong currency. Therefore, it is necessary to assess the exchange rate volatility risk in the context of direct investment in order to develop preventive policy routes that would encourage foreign investors into the country. To this purpose, the autoregressive distributive least square (ARDL) technique has been employed to investigate the symmetric effect of exchange rate volatility on foreign direct investment (FDI) during global financial crises and political regimes from January 2000 to December 2018. In order to eliminate arbitrariness, the study uses the most accredited estimate of volatility, GARCH (1 1), as part of the re-estimation process. Besides this, the interaction has been studied under various regimes to see how the political environment affects foreign market participants’ expectations for future gains. The findings suggest that exchange rate volatility is adversely related to FDI and is a source of decreased net foreign investment in Pakistan. It also illustrates that during times of crises and apolitical regimes, Pakistan’s average FDI falls dramatically. The findings are extended to the context of Pakistan that has seen significant rupee volatility for the past few years. Our study recommends that policymakers should pursue exchange rate measures that promote exchange rate stability, which might assist to minimize risk of exchange rate volatility and so attract higher FDI. It is also crucial to formulate more sustainable investment methods that allow for efficient capital allocation during times of economic uncertainty.

Complicated functions appearing in physics are frequently simplified by a symmetrical parabolic approximation for obtaining useful results. The symmetrical parabolic approximation is employed in many different problems in a first year college physics course. Some examples of this approximation are explored in this article. With the aid of Hamilton’s equations it is shown that the classical formula for the kinetic energy of a particle is a symmetrical parabolic approximation for the more general relativistic formula.

There is currently a growing interest in understanding which lattice simplices have uni-modal local h^*-polynomials (sometimes called box polynomials); specifically in light of their potential applications to unimodality questions for Ehrhart h^*-polynomials. In this note, we compute a general form for the local h^*-polynomial of a well-studied family of lattice simplices whose associated toric varieties are weighted projective spaces. We then apply this formula to prove that certain such lattice simplices, whose combinatorics are naturally encoded using common systems of numeration, all have real-rooted, and thus unimodal, local h^*-polynomials. As a consequence, we discover a new restricted Eulerian polynomial that is real-rooted, symmetric, and admits intriguing number theoretic properties.

In the third week of the 2018 Summer Workshop on Lattice Polytopes at Osaka University, the authors lead an open problem session. In this note, we describe the open problems discussed at this session.

Based on the unitization of pseudoeffect algebras, we will give the necessary and sufficient conditions such that lattice operations of a generalized pseudo-effect algebra P are inherited in its unitization .

The complex structure of low-lying as well as those of high-lying states is discussed within multiphonon approach. The approach is based on Quasiparticle-Phonon Model. This microscopic model goes beyond the quasiparticle random-phase approximation by treating a Hamiltonian of separable form in a microscopic multiphonon basis. It is therefore able to describe the anharmonic features of collective modes. In the case of low-lying part of excitations the model has close correspondence with the proton-neutron interacting boson model. Within the model highly-excited single-particle states in nuclei are coupled with the excitations of a more complex character, first of all with collective phonon-like modes of the core. Although, on the level of one and two-phonon admixtures, the fully chaotic GOE regime is not reached, the eigenstates of the model carry significant degree of complexity that can be quantified with the aid of correlation invariant entropy.