Nonnegative Power Research Articles

Variation of Distributed Power Control Algorithm in Co-Tier Femtocell Network

The wireless communication network has seen rapid growth, especially with the widespread use of smartphones, but resources are increasingly limited, especially indoors. Femtocell, a spectrum-efficient small cellular network solution, faces challenges in distributed power control (DPC) when deployed with distributed users, impacting power levels, and causing interference in the main network. The aim of this research is optimizing user power consumption in co-tier femtocell networks by using the user power treatment. This study proposed the Distributed Power Control (DPC) variation methods such as Distributed Constrained Power Control (DCPC), Half Distributed Constrained Power Control (HDCPC), and Generalized Distributed Constrained Power Control (GDCPC) in co-tier femtocell network. The research examines scenarios where user power converges but exceeds the maximum threshold or remains semi-feasible, considering factors like number of users, distance, channel usage, maximum power values, non-negative power vectors, Signal-to-Interference-plus-Noise Ratio (SINR), and link gain matrix values. In Distributed Power Control (DPC), distance and channel utilization affect feasibility conditions: feasible, semi-feasible, and non-feasible. The result shows that Half Distributed Constrained Power Control (HDCPC) is more effective than Distributed Constrained Power Control (DCPC) in semi-feasible conditions due to its efficient power usage and similar Signal-to-Interference-plus-Noise Ratio (SINR). Half Distributed Constrained Power Control (HDCPC) is also easier to implement than Generalized Distributed Constrained Power Control (GDCPC) as it does not require user deactivation when exceeding the maximum power limit. Distributed Power Control (DPC) variations can shift the power and Signal-to-Interference-plus-Noise Ratio (SINR) conditions from non-convergence to convergence at or below the maximum power level. We concluded that the best performance of Distributed Power Control (DPC) is Half Distributed Constrained Power Control (HDCPC).

ANALYTICAL CALCULATION OF A BEAM BASED ON AN ELASTIC WINKLER FOUNDATION WITH RANGE INHOMOGENITY

The aim of the study is the further development of analytical methods for calculating the bending of beams resting on a non-homogeneous continuous Winkler elastic foundation. This paper considers the case when the beam is under the influence of a uniformly distributed constant transverse load, and the inhomogeneity of the elastic foundation is given by a power function with an arbitrary non-negative power exponent . Fundamental functions and a partial solution of the corresponding differential equation of beam bending are found in an explicit closed form. These functions are dimensionless and are represented by absolutely and uniformly convergent power series. In turn, the formulas for the parameters of the stress-strain state of the beam – deflection, angle of rotation, bending moment and transverse force – are expressed through the indicated functions. The unknown constants of integration in these formulas are expressed in terms of the initial parameters, which are after the implementation of the specified boundary conditions. Thus, the calculation of the beam for bending is reduced to the procedure of numerical implementation of explicit analytical formulas for the parameters of the stress-strain state. An example demonstrates the practical application of the obtained solutions. A prismatic concrete beam based on a cubic variable elastic foundation is considered. This case corresponds to the power value . The results of the calculation by the author's method are presented in numerical and graphical formats for the case when the left end of the beam is hinged and the right end is clamped. The numerical values obtained by the author's method are accurate, since the applied calculation method is based on the exact solution of the corresponding differential equation. The availability of such solutions makes it possible to evaluate the accuracy of solutions obtained using various approximate methods by comparison. For the purpose of such a comparison, the paper presents the calculation results obtained by the finite element method (FEM). The absolute error of the FEM method when calculating this design was determined.

Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices

By considering the tiling of an N-board (a linear array of N square cells of unit width) with new types of tile that we refer to as combs, we give a combinatorial interpretation of the product of two consecutive generalized Fibonacci numbers s n (where s n = ∑ i = 1 q v i s n − m i , s 0 = 1 , s n < 0 = 0 , where v i and m i are positive integers and m 1 < ⋯ < m q ) each raised to an arbitrary non-negative integer power. A ( w , g ; m ) -comb is a tile composed of m rectangular sub-tiles of dimensions w × 1 separated by gaps of width g. The interpretation is used to give combinatorial proof of new convolution-type identities relating s n 2 for the cases q = 2, v i = 1 , m 1 = M , m 2 = m + 1 for M = 0, m to the permanent of a (0,1) Toeplitz matrix with 3 nonzero diagonals which are − 2 , M−1, and m above the leading diagonal. When m = 1, these identities reduce to ones connecting the Padovan and Narayana's cows numbers.

DC Power Grids With Constant-Power Loads—Part II: Nonnegative Power Demands, Conditions for Feasibility, and High-Voltage Solutions

In this two-part article, we develop a unifying framework for the analysis of the feasibility of the power flow equations for dc power grids with constant-power loads. Part II of this article, explores further implications of the results in Part I. We present a necessary and sufficient linear matrix inequality (LMI) condition for the feasibility of a vector of power demands (under small perturbation), which extends a necessary condition in the literature. The alternatives of these LMI conditions are also included. In addition, we refine these LMI conditions to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which allows for an alternative approach to determine power flow feasibility. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. Finally, we prove that the unique long-term voltage semistable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is obtained, as well as a parametrization of the boundary of the set of feasible power demands.

Signal clipping at transmitter and receiver of O-OFDM for VLC under optical power constraint

Visible light communications (VLC) is considered as an effective supplement technology for next-generation (6G) communications due to its abundant spectrum, high power efficiency and easy deployment. Optical orthogonal frequency division multiplexing (O-OFDM) is a common technology to obtain further promotion. In this paper, two typical O-OFDM schemes direct current biased O-OFDM (DCO-OFDM) and asymmetrically clipped O-OFDM (ACO-OFDM) are analyzed in terms of signal clipping at both transmitter and receiver under the constraints of maximum optical power and non-negative optical power. And effective electrical SNR models after signal clipping are proposed and verified by link simulation. Then a noise cancellation scheme is proposed based on received signal clipping and is proved to bring a significant gain for ACO-OFDM. By system simulation, we find that under a certain optical power limitation, most users can achieve above 4Gbps in indoor scenario when modulation bandwidth of the light emit diode (LED) or laser diode (LD) is 1GHz. Therefore, it can be expected that the throughput could reach tens Gbps when the LED/LD modulation bandwidth is increased and multiple LEDs/LDs are deployed.

Power graph of a finite group is always divisor graph

The power graph is a special type undirected simple graph of a finite group G which has the group elements as its vertex set and two distinct vertices [Formula: see text] are adjacent if one is non-negative integral power of other. Vertex labeling of graph [Formula: see text] is a process of assigning integers to all its vertices subject to certain conditions. In simple words, vertex (edge) labeling is a function of all vertices (edges) to set of labels. Frequently, integers are used in labeling of vertices and edges. A graph [Formula: see text] is said to be divisor graph if all vertices of graph can be labeled with positive integers such that any two distinct vertices [Formula: see text] are adjacent if and only if either [Formula: see text] or [Formula: see text]. In this research paper, we prove that every power graph of finite group is always a divisor graph, but converse is not true.

Research on Electrochemical Machining of Small Deep Holes with Positive and Negative Pulse Power

Background: High-temperature alloys, such as the nickel-based alloy, have become the main materials for core components in the aerospace field because of their high strength and good toughness. Therefore, how to improve the machining accuracy and stability of electrochemical machining (ECM) of small deep holes on nickel-based alloy is an important topic for studies. The instantaneous high-density current during the pulse width of pulse ECM is beneficial to the dissolution of nickel-based alloy. Many experts and scholars have studied pulse ECM of small deep holes. Objective: The purpose of this article is to propose and design a positive and negative pulse (PANP) power supply to study the accuracy and stability of ECM of small deep holes on the nickel-based alloy. Methods: First of all, an H-bridge composed of four MOSFET switches is designed to achieve PANP output in the main circuit of the power supply. Then, this article discusses the influence of the ratio of positive and negative pulses on short circuits, the influence of the ratio of positive and negative pulses on the mass removal rate, and the influence of the electrolyte concentration and pulse width on the mass removal rate. Finally, according to the obtained optimal parameters, the influence of the electrolyte pressure on the average radial overcut of hole depth is analyzed. Results: The experimental results show that the short-circuit frequency is reduced by more than 50% compared with non-negative pulses power supply; the ratio of positive and negative pulses, pulse width, and electrolyte concentration and pressure were optimized by experiments in order to improve the mass removal rate of the workpiece and the average radial overcut of hole depth. Conclusion: The designed PANP power supply can improve the machining accuracy and stability of ECM of small deep holes on the nickel-based alloy.

Feasibility Analysis of Distributed Power Control System for Cognitive Radio Networks

The need for an efficient transmit power is affected by the condition of user and power control methods used. User conditions that categorized in cognitive femtocell networks included in the category as distributed user, so it required a distributed power control (DPC). To be implemented in cognitive radio network (CRN) communication, the system must be feasible. The problem raised in this research regarding the feasibility of implementing the DPC system on the CR network To meet the feasible requirements, it is necessary to test the system's feasibility through testing the eigenvalues of the link gain matrix obtained and testing the non-negative power vector conditions. In this study, experiments were carried out on 2 schemes of the number of users, namely the scheme of 5 users and 10 users, to determine the power requirements of each user according to the channel distribution. The results obtained for both schemes show that the total eigenvalue of the link gain matrix for all channels is less than 1 and all users meet the non-negative power vector requirements. So it can be concluded that those two schemes are feasible to implement a distributed power control system. Furthermore, as more users use the channel and the closer the distance between users, the more power is consumed due to high interference, necessitating high power compensation in order to maintain the target of signal to interference and noise ratio (SINR).

Endpoint symmetries of helicity amplitudes

We investigate helicity amplitudes (HAs) of A→BC-type decays for arbitrary spin towards the kinematic endpoint. We show that HAs are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to a non-negative power. The latter can be zero in which case the HA is non-vanishing at the endpoint. At the kinematic endpoint the explicit breaking of rotational symmetry, through the external momenta, is restored and the findings can be interpreted as a special case of the Wigner-Eckart theorem. Our findings are useful for i) checking theoretical computations and ii) the case where there is a sequence of decays, say B→B1B2 with the pair (B1B2) not interacting (significantly) with the C-particle. Angular observables, which are ratios of HAs, are given by ratios of CGC at the endpoint. We briefly discuss power corrections in the velocity to the leading order.

Recurrent neural network-based multiaxial plasticity model with regularization for physics-informed constraints

A recurrent neural network (RNN) based model is developed as a surrogate to predict nonlinear plastic response under multiaxial loading. The RNN-based model is trained and tested on stress versus strain curves generated using a numerical solution based on the classical radial return method. Besides simply learning the basic constitutive relationship, a novel approach is taken to enforce certain physical conditions. Specifically, regularization is employed to maintain non-negative plastic power density throughout the loading history thereby ensuring monotonically increasing plastic work and thermodynamic consistency. Enforcing physics in this manner permits coupling of the data-driven RNN approach with physics-based knowledge and laws. This has the effect of reducing the necessary amount of data and ensuring known physical laws are not violated. Since, once trained, the model need not perform the expensive task of solving nonlinear equations, its efficiency is orders of magnitude greater than its numerical counterpart. The RNN-based model has been trained on varied sets of data and the accuracy on test datasets validated. The developed model is general and robust and has widespread application such as in the simulation of metal forming, large scale plasticity, and part life prediction.

Non-negative Integer Power of a Hyponormal m-isometry is Reflexive

Sarason did pioneer work on reflexive operator and reflexivity of normal operators, however, he did not used the word reflexive but his results are equivalent to say that every normal operator is reflexive. The word reflexive was suggested by HALMOS and first appeared in H. Rajdavi and P. Rosenthals book `Invariant Subspaces’ in 1973. This line of research was continued by Deddens who showed that every isometry in B(H) is reflexive. R. Wogen has proved that `every quasi-normal operator is reflexive’. These results of Deddens, Sarason, Wogen are particular cases of theorem of Olin and Thomson which says that all sub-normal operators are reflexive. In other direction, Deddens and Fillmore characterized these operators acting on a finite dimensional space are reflexive. J. B. Conway and Dudziak generalized the result of reflexivity of normal, quasi-normal, sub-normal operators by proving the reflexivity of Vonneumann operators. In this paper we shall discuss the condition under which m-isometries operators turned to be reflexive.

Large-time Behavior of Magnetohydrodynamics with Temperature-Dependent Heat-Conductivity

For the strong solutions to the equations of a planar magnetohydrodynamic compressible flow with the heat conductivity proportional to a nonnegative power of the temperature, we first prove that both the specific volume and the temperature are proved to be bounded from below and above independently of time. Then, we also show that the global strong solution is nonlinearly exponentially stable as time tends to infinity. This is the first result obtaining the exponential stability behavior of strong solutions to the equations of a planar magnetohydrodynamic compressible flow without any smallness conditions on the data. Our result can be regarded as a natural generalization of the previous ones for the compressible Navier-Stokes system to MHD system with either constant heat-conductivity or nonlinear and temperature-depending heat-conductivity. As a direct consequence, it is shown that the global strong solution to the constant heat-conductivity MHD system whose existence is obtained by Kazhikhov in 1987 is nonlinearly exponentially stable.

Nikol’skii–Bernstein Constants for Entire Functions of Exponential Spherical Type in Weighted Spaces

We study the exact constant in the Nikol’skii–Bernstein inequality $$\|Df\|_{q}\leq C\|f\|_{p}$$ on the subspace of entire functions $$f$$ of exponential spherical type in the space $$L^{p}(\mathbb{R}^{d})$$ with a power-type weight $$v_{\kappa}$$ . For the differential operator $$D$$ , we take a nonnegative integer power of the Dunkl Laplacian $$\Delta_{\kappa}$$ associated with the weight $$v_{\kappa}$$ . This situation encompasses the one-dimensional case of the space $$L^{p}(\mathbb{R}_{+})$$ with the power weight $$t^{2\alpha+1}$$ and Bessel differential operator. Our main result consists in the proof of an equality between the multidimensional and one-dimensional weighted constants for $$1\leq p\leq q=\infty$$ . For this, we show that the norm $$\|Df\|_{\infty}$$ can be replaced by the value $$Df(0)$$ , which was known only in the one-dimensional case. The required mapping of the subspace of functions, which actually reduces the problem to the radial and, hence, one-dimensional case, is implemented by means of the positive operator of Dunkl generalized translation $$T_{\kappa}^{t}$$ . We prove its new property of analytic continuation in the variable $$t$$ . As a consequence, we calculate the weighted Bernstein constant for $$p=q=\infty$$ , which was known in exceptional cases only. We also find some estimates of the constants and give a short list of open problems.

Hardness of Minimum Barrier Shrinkage and Minimum Installation Path

In the Minimum Installation Path problem, we are given a graph G with edge weights w(⋅) and two vertices s,t of G. We want to assign a non-negative power p:V→R≥0 to the vertices of G, so that the activated edges {uv∈E(G)|p(u)+p(v)≥w(uv)} contain some s-t-path, and minimize the sum of assigned powers. In the Minimum Barrier Shrinkage problem, we are given, in the plane, a family of disks and two points x and y. The task is to shrink the disks, each one possibly by a different amount, so that we can draw an x-y curve that is disjoint from the interior of the shrunken disks, and the sum of the decreases in the radii is minimized.We show that the Minimum Installation Path and the Minimum Barrier Shrinkage problems (or, more precisely, the natural decision problems associated with them) are weakly NP-hard.

CORRELATIONAL ANALYSIS OF POLLUTANT EMISSION INTENSITY IN VARIOUS CONDITIONS OF OPERATION OF THE AUTOMOTIVE INTERNAL COMBUSTION ENGINE

The aim of this article was to analyse the correlation of emission intensity of carbon monoxide, hydrocarbons, nitrogen oxides, and carbon dioxide in various conditions of operation of the automotive internal combustion engine. The operational properties of the engine were investigated on chassis dynamometer in driving test cycles simulating various real-world conditions of the vehicle drive: street congestions, urban traffic without congestions, extra-urban traffic, and high-speed traffic. The correlational dependence of the pollutant emission intensity on the non-negative effective power of the engine and the correlational interdependence between the emission intensity of individual pollutants were investigated. The coefficients of Pearson’s linear correlation, Spearman’s rank correlation, Kruskal’s gamma correlation, and Kendall’s tau correlation were calculated. It was found that the emission intensity of pollutants in the driving test cycles strongly depends on the dynamic states of operation of the engine. The time histories of the emission intensity of pollutants were strongly correlated with the non-negative effective power of the engine. There were only a few cases where this correlation can be assessed as weak. The time histories of the emission intensity of individual pollutants were also strongly correlated with each other, with only a few exemptions.

A Metanilpotency Criterion for a Finite Solvable Group

Denote by |x| the order of an element x of a group. An element of a group is called primary if its order is a nonnegative integer power of a prime. If a and b are primary elements of coprime orders of a group, then the commutator a−1b−1ab is called a *-commutator. The intersection of all normal subgroups of a group such that the quotient groups by them are nilpotent is called the nilpotent residual of the group. It is established that the nilpotent residual of a finite group is generated by commutators of primary elements of coprime orders. It is proved that the nilpotent residual of a finite solvable group is nilpotent if and only if |ab| ≥ |a||b| for any *-commutators of a and b of coprime orders.

Distribution of entanglement in multipartite systems

Distribution of entanglement for the multipartite systems is characterized through monogamy and polygamy relations. In this paper, we study the xth power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations based on the nonnegative power of Tsallis-q entanglement are obtained for N-qubit states and are shown to be tighter than existing relation. We find that for any tripartite mixed state, the Tsallis-q entanglement follows a polygamy relation. This polygamy relation also holds for the multi-qubit systems. The polygamy relations of the Tsallis-q entanglement, that are uniquely defined for generalized multi-qubit W-class states, and partially coherent superposition states are also examined. Moreover, the tighter monogamy bounds for concurrence of assistance and negativity of assistance are also established for these states, which gives more accurate bounds than existing relations.

Wave Correction Scheme for Task Space Control of Time-Varying Delayed Teleoperation Systems

This brief presents a novel method in wave variable approach for controlling the $SE(3)$ task space manipulation of the teleoperation system over time-varying delayed communication. The scheme modulates typical wave commands using corrective waves to address the motion/effort mismatch largely caused by time-varying delay and environmental impedance. These corrections are computed based on the difference between the desired and fictitious poses obtained from integrating/propagating nondistorted wave variables. Resulting waves ensure the pose and, moreover, effort tracking of the teleoperation system under appropriate conditions. Passivity of the system is guaranteed by the nonnegative power dissipation constraint on the corrective wave signals, or by the help of dissipative elements in the controllers. Therefore, the scheme may be integrated to the master/slave robots controlled with passive motion/force controllers. Specific application to the teleoperation system with the proportional–derivative controllers is studied.

Hamming weight and tight constraints of multi-qubit entanglement in terms of unified entropy

We establish a characterization of multi-qubit entanglement constraints in terms of non-negative power of entanglement measures based on unified-(q, s) entropy. Using the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of tight monogamy inequalities of multi-qubit entanglement based on the αth-power of unified-(q, s) entanglement for α ≥ 1. For 0 ≤ β ≤ 1, we establish a class of tight polygamy inequalities of multi-qubit entanglement in terms of the βth-power of unified-(q, s) entanglement of assistance. Thus our results characterize the monogamy and polygamy of multi-qubit entanglement for the full range of non-negative power of unified entanglement.

Optimizing power allocation in wireless networks: Are the implicit constraints really redundant?

The widely considered power constraints on optimizing power allocation in wireless networks, e.g., non-negative individual power and limited sum of all the individual power, imply the constraints where each individual power is not greater than the limited sum. However, the related implicit constraints are generally regarded as redundant for algorithm design in most current studies. In this paper, we explore the question “Are the implicit constraints really redundant?” in the optimization of power allocation especially when using iterative methods (e.g., subgradient method) that have slow convergence speeds. Using the water-filling problem as an illustration, we first derive the structural properties of the optimal solutions based on Karush–Kuhn–Tucker conditions. Then we propose a non-iterative closed-form optimal method and use iterative methods (i.e., bisection method and subgradient method) to solve the problem. Our theoretical analysis shows that the implicit constraints are not redundant, and particularly, their consideration can effectively speed up the convergence of the subgradient method and reduce its sensitivity to the chosen step size. Numerical results for the water-filling problem and another existing power allocation problem demonstrate the effectiveness of considering the implicit constraints.