Unary Operation Research Articles

Research on the Architecture of Service-oriented Space Ground Transmission Computer Network

With the rapid development of microelectronic technology, avionics system is gradually developing to Integrated Modular Avionics (IMA) system, which is a way to share multiple subsystems through a unified network connection. Therefore, we need to integrate several kinds of standard module resources and carry out terrestrial transmission. Therefore, aerospace must establish a service-oriented ground transmission computer network system, which will form a unified platform for information processing and message exchange. By supporting highly integrated avionics functions, we can achieve results in functional performance, operational performance and affordable cost. Therefore, based on the typical embedded computer information system, this paper proposes a service-oriented terrestrial transmission network architecture, which will enhance the dynamic allocation of terrestrial transmission network resources. By enhancing the unified operation and maintenance and security control, we can continuously increase the demand of various kinds of aerospace business.

Similarity monadic basic logic

The present study aimed to investigate the similarity monadic $BL$-algebras and prove the completeness of the similarity monadic basic logic. To this end, the similarity monadic $BL$-algebras were defined as: a variety of monadic $BL$-algebras equipped with unary operators $\forall$ and $\exists$, and the vital properties of the algebras were provided. In addition, the S-monadic filters in the similarity monadic $BL$-algebras were introduced and investigated. Correspondingly, the representable similarity monadic $BL$-algebras were characterized, and the notion of the logic of the similarity monadic $BL$-algebras were introduced to prove their soundness and completeness.

Environmentally Friendly Methods for Flavonoid Extraction from Plant Material: Impact of Their Operating Conditions on Yield and Antioxidant Properties.

The flavonoids are compounds synthesized by plants, and they have properties such as antioxidant, anticancer, anti-inflammatory, and antibacterial, among others. One of the most important bioactive properties of flavonoids is their antioxidant effect. Synthetic antioxidants have side toxic effects whilst natural antioxidants, such as flavonoids from natural sources, have relatively low toxicity. Therefore, it is important to incorporate flavonoids derived from natural sources in several products such as foods, cosmetics, and drugs. For this reason, there is currently a need to extract flavonoids from plant resources. In this review are described the most important parameters involved in the extraction of flavonoids by unconventional methods such as ultrasound, pressurized liquid extraction, mechanochemical, high hydrostatic pressure, supercritical fluid, negative pressure cavitation, intensification of vaporization by decompression to the vacuum, microwave, infrared, pulsed electric field, high-voltage electrical discharges, and enzyme-assisted extraction. There are no unified operation conditions to achieve high yields and purity. Notwithstanding, progress has been achieved in the development of more advanced and environmentally friendly methods of extraction. Although in literature are found important advances, a complete understanding of the extraction process in each of the unconventional techniques is needed to determine the thermodynamic and kinetic mechanisms that govern each of the techniques.

Optimal radio-[formula omitted]-labelings of trees

Let G be a graph, and let k be a positive integer. The radio-k-number of G is the smallest integer s for which there exists a function f:V(G)→{0,1,2,…,s} such that for any two vertices u,v∈V(G), |f(u)−f(v)|⩾k+1−d(u,v), where d(u,v) is the distance between u and v. In particular, when d is the diameter of G, the radio-d-number is called the radio number of G. This article contains four major parts. First, we extend Liu’s lower bound on radio numbers of trees to radio-k-numbers of trees. We call a tree whose radio-k-number is equal to this lower bound a k-lower bound tree. Second, we establish properties of k-lower bound trees, and apply these properties to obtain shorter proofs and generalizations of some known results. Third, we investigate the minimum integer k such that a given tree T is a k-lower bound tree. Fourth, we define the joined union operation on trees, where trees are composed by merging a vertex from each tree into a single vertex. We use this operation to construct new k-lower bound trees in three ways. Finally, we pose several questions for future study.

Extensions of dynamic programming for multi-stage combinatorial optimization

We propose a dynamic programming framework for an exact multi-stage (lexicographic) combinatorial optimization. Unlike conventional algorithms of dynamic programming that return one optimal solution, two dynamic programming algorithms proposed in this paper are coping with the whole set of optimal solutions or with its essential part. We describe the set of elements for optimization by a labeled directed acyclic graph, which in some sense, is similar to the structure of subproblems of the considered problem. For a given cost function (objective), the first algorithm constructs a subgraph of this graph that describes the whole set of optimal elements or its essential part. This algorithm can be used for multi-stage optimization of elements relative to a sequence of cost functions. The second algorithm counts elements before the optimization and after each optimization step. The considered labeled directed acyclic graph is a kind of circuit. This circuit builds the set of elements for optimization from one-element sets attached to input nodes. It uses the operation of union of sets attached to unifying nodes and functional operations attached to functional nodes. The algorithms for optimization and counting elements are defined for an arbitrary circuit without repetitions in which each element is generated exactly one time. For a considered problem with a known conventional dynamic programming solution algorithm, usually, it is easy to construct a corresponding circuit without repetitions. Once the circuit and cost functions are defined, our framework provides the correctness proofs and detailed time complexity analysis for the proposed algorithms. To make this approach more intuitive, we consider an illustrative example related to the maximum subarray problem. We tested our approach on the following nine combinatorial optimization problems: matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, optimal bitonic tour, segmented least squares, convex polygon triangulation, one-dimensional clustering, and line breaking (text justification). We consider the last three problems in detail: construct a circuit without repetitions, describe at least two cost functions, evaluate a number of operations and time required by the algorithms, discuss an example, and consider the results of computer experiments with randomly generated instances of the problem.

NPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multi-fidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(y), which is more suitable for modeling wall-bounded turbulence, e.g. turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

Admissible Galois Structures on the categories dual to some varieties of universal algebras

Abstract The subject of the paper is suggested by G. Janelidze and motivated by his earlier result giving a positive answer to the question posed by S. MacLane whether the Galois theory of homogeneous linear ordinary differential equations over a differential field (which is Kolchin–Ritt theory and an algebraic version of Picard–Vessiot theory) can be obtained as a particular case of G. Janelidze’s Galois theory in categories. One ground category in the Galois structure involved in this theory is dual to the category of commutative rings with unit, and another one is dual to the category of commutative differential rings with unit. In the present paper, we apply the general categorical construction, the particular case of which gives this Galois structure, by replacing “commutative rings with unit” by algebras from any variety V \mathscr{V} of universal algebras satisfying the amalgamation property and a certain condition (of the syntactical nature) for elements of amalgamated free products which was introduced earlier, and replacing “commutative differential rings with unit” by V \mathscr{V} -algebras equipped with additional unary operations which satisfy some special identities to construct a new Galois structure. It is proved that this Galois structure is admissible. Moreover, normal extensions with respect to it are characterized in the case where V \mathscr{V} is any of the following varieties: abelian groups, loops and quasigroups.

Completeness and normal form of multi-valued logical functions

Theory of completeness is essential for multi-valued logical functions. Using semi-tensor product (STP) of matrices, the algebraic form of k-valued logical functions is presented. Using algebraic form, a method is proposed to construct an adequate set of connectives (ASC), consisting of unary operators with conjunction/disjunction for k-valued logical functions, which can be used to express any k-valued logical functions. Based on it, two normal forms of k-valued logical functions are presented, which are extensions of the disjunctive normal form and conjunctive normal form of Boolean functions respectively. The ASC is then simplified to a condensed set. Finally, the normal forms are further extended to mix-valued logical functions.

Inequalities for a Unified Integral Operator via α,m-Convex Functions

Recently, a unified integral operator has been introduced by Farid, 2020, which produces several kinds of known fractional and conformable integral operators defined in recent decades (Kwun, 2019, Remarks 6 and 7). The aim of this paper is to establish bounds of this unified integral operator by means of α,m-convex functions. The resulting inequalities provide the bounds of all associated fractional and conformable integral operators in a compact form. Also, the results of this paper hold for different kinds of convex functions connected with α,m-convex functions.

Approaches in Design of Laboratory-Scale UASB Reactors

Up-flow Anaerobic Sludge Blanket (UASB) reactors are popular tools in wastewater treatment systems due to the ability to work with high feed rates and wastes with high concentration of organic contaminants. While full-scale industrial applications of UASB reactors are developed and described in the available literature, laboratory-scale designs utilized for treatability testing are not well described. The majority of published studies do not describe the laboratory UASB construction details or do use reactors that already had developed a trophic network in microbial consortia under laboratory environment and therefore are more stable. The absence of defined guidelines for geometry design, selection of materials, construction, operation rules, and, especially, the start-up conditions, significantly hamper researchers who desire to conduct treatability testing using UASB reactors in laboratory scale. In this article, we compiled and analyzed the information available in the refereed literature concerning UASB reactors used in laboratory environment, where information on geometry and/or operational conditions were provided in detail. We utilized the information available in the literature and the experience gained in our laboratory (Sustainable Waste to Bioproducts Engineering Center) to suggest a unified operation flowchart and for design, construction, operation, and monitoring for a laboratory-scale UASB reactors.

On a unified integral operator for \u03c6-convex functions

Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use φ-convex functions for unified integral operators to obtain their upper bounds and upper and lower bounds for symmetric φ-convex functions in the form of a Hadamard inequality. Also, for φ-convex functions, we obtain bounds of different known fractional and conformable fractional integrals. The results of this paper are applicable to convex functions.

Design of Efficient Ternary Operators for Scrambling in CNTFET Technology

Digital computation using ternary logic allows compact and energy-efficient digital design due to the reduction in circuit interconnects and chip area. CNFET unique characteristic of scalable threshold voltage value by utilizing the CNTs of different chirality vectors makes it a suitable option to realize ternary logic designs. This work presents hardware-efficient and low-power ternary operators exclusively used for scrambling applications in crypto-algorithms. The proffered designs are based on multiplexing the output digits among various unary cycle operators as the input trits. Extensive HSPICE simulations are conducted using standard 32-nm CNFET Stanford model to calculate the performance parameters of the proposed circuits. The presented designs show a significant improvement in terms of average power consumption, component count and energy consumption as compared to earlier counterparts. Results for various proposed scrambling operators Sop3, Sop4 and Sop5 show about an average reduction in energy consumption of 80% as compared to previously presented scrambling operators. Moreover, the Monte Carlo simulation results reveal that the proposed designs are robust against the mismatches in the diameter of CNTs.

The role of states in triangle algebras

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. Using this concept, we definetwo types IVRL-extended $sigma$-filters of a state trianglealgebra.

M-VCUT level set method for optimizing cellular structures

This paper presents a multiple variable cutting (M-VCUT) level set method for the topology optimization of cellular structures. This method first divides the reference design domain into cells, and then in each cell it uses multiple basic level set functions combined with their cutting functions to describe the microstructure. The basic level set functions are used to describe microstructure prototypes that are kept fixed during the course of optimization. Each basic level set function is cut by its own cutting function to achieve shape and topology variation of microstructure. After the cutting operations, multiple virtual microstructures are obtained in each cell, and they are further combined together through a union operation to generate an actual microstructure. Based on the multiple virtual microstructures, multiple combination options are available, thus resulting in an enlarged design space and performance improvement as compared to the VCUT level set method developed in our previous study. Moreover, as a generalization of the VCUT level set method, connections between microstructures in neighboring cells are naturally guaranteed without any extra constraints.

Bounds of a Unified Integral Operator via Exponentially s,m-Convexity and Their Consequences

Various known fractional and conformable integral operators can be obtained from a unified integral operator. The aim of this paper is to find bounds of this unified integral operator via exponentially s,m-convex functions. The resulting bounds provide compact formulas for the bounds of associated fractional and conformable integral operators. Several Hadamard-type inequalities have been produced from a compact version for unified integral operators for exponentially s,m-convex functions.

Dynamic programming bi-criteria combinatorial optimization

We introduce a model for combinatorial optimization problems based on the notion of a circuit. This circuit builds a set of elements for optimization from one-element sets attached to input nodes. It uses the operation of union of sets and functional operations on elements extended to sets of elements. We design a dynamic programming algorithm based on this circuit which constructs the set of Pareto optimal points for the problem of bi-criteria optimization of elements described by the circuit relative to two cost functions. We tested this approach on nine known combinatorial optimization problems. The problems related to the matrix chain multiplication, optimal paths in directed graphs, and binary search trees are considered in detail.

A Union Operation of Non-Dominated K-Coterie in Distributed System

Coterie is a set of quorums which has non-empty intersections and are not part of other quorum. The natural development of the coterie system is k-coterie. The k-coterie consists of 2 types, that are non-dominated k-coterie and dominated k-coterie. The non-dominated k-coterie is more resilient to failure than the dominated k-coterie. Combining two non-dominated k-coterie by applying union operation can result the dominated k-coterie. This study aims to define a combination of the non-dominated k-coterie with non-dominated k-coterie using the expanded union operation. The merger of non-dominated k-coterie with the non-dominated k-coterie produces a non-dominated k-coterie.

Development of an ESMF Based Flexible Coupling Application of ADCIRC and WAVEWATCH III for High Fidelity Coastal Inundation Studies

To enable flexible model coupling in coastal inundation studies, a coupling framework based on the Earth System Modeling Framework (ESMF) and the National Unified Operational Prediction Capability (NUOPC) technologies under a common modeling framework called the NOAA Environmental Modeling System (NEMS) was developed. The framework is essentially a software wrapper around atmospheric, wave and storm surge models that enables its components communicate seamlessly, and efficiently to run in massively parallel environments. For the first time, we are introducing the flexible coupled application of the ADvanced CIRCulation model (ADCIRC) and unstructured fully implicit WAVEWATCH III including NUOPC compliant caps to read Hurricane Weather Research and Forecasting Model (HWRF) generated forcing fields. We validated the coupled application for a laboratory test and a full scale inundation case of the Hurricane Ike, 2008, on a high resolution mesh covering the whole US Atlantic coast. We showed that how nonlinear interaction between surface waves and total water level results in significant enhancements and progression of the inundation and wave action into land in and around the hurricane landfall region. We also presented that how the maximum wave setup and maximum surge regions may happen at the various times and locations depending on the storm track and geographical properties of the landfall area.

Assessing the performance of Canadian credit unions using a three-stage network bootstrap DEA

We use a novel three-stage network data envelopment analysis (DEA) model (based on production, intermediation, and revenue generation operations) with bootstrapping to evaluate the performance of 14 of the largest Canadian credit unions for the period 2007–2017 and the impact of various events on this performance. For each analysis, we contrast the results of the network DEA with those of a black box DEA. We show that the former provides more insightful information regarding the sources of the inefficiencies. We first found that while overall, the credit unions showed high-efficiency ratios, there is room for improvement, especially for the production sub-process. Moreover, the efficiency of individual credit unions is not consistent across the three different stages. Through the years 2007–2017, the credit union system exhibits a relatively sharp decline in its efficiency, mainly due to managerial issues at the revenue generation stage. Our analyses show that the various stages of Canadian credit union operations have been affected by the 2007–2009 financial crisis, the low policy interest rates that occurred in the following years, and the fact that in Canada, the federal government has eliminated the discount on the federal tax rate. The credit unions can improve their performance at the different stages by exploring Fintech Solutions to reduce their operating costs, seeking a better mix of loans and securities investments, and improving their interest and saving rate settings.

Потребительская кооперация Башкирии в период проведения денежной реформы 1947 г.

The paper deals with the development of consumer cooperation in Bashkiria in the post-war years. Based on documents of the National Archive of the Republic of Bashkortostan, which had never been subjected to scientific scrutiny, the study traces the growth of sales, spreading the trading network and storage facilities of consumer cooperation in the period immediately before the monetary reform of 1947. In the post-war period, consumer cooperation in Bashkiria showed considerable achievements. On the one hand, commodity weight rose significantly with the simultaneous expansion and complication of the trading network. On the other hand, the assortment of foodstuffs and manufactured goods was expanding, which was a prerequisite for the transition from rationing to open trade. However, the research disclosed some significant flaws in the work of consumer societies in the Republic. Accounting and statistical documents of Bashkir Union contain information about great damage from embezzlements and thefts as well as a large number of the principles of Soviet trade violations. Cooperation and share accumulation were not fully followed, which negatively affected the financial state of consumer cooperatives. On all levels of consumer cooperation in the Republic, there was a lack of qualified staff. Due to this, buying and producing operations of some regional consumer cooperation unions lead to an increase in the amount of low-demand, old-stock goods in the trading network, and often to material losses. Those many problems in the work of consumer cooperation led to the insufficient satisfaction of demands for both food stocks and manufactured goods. This, in turn, affected the welfare of city and country people in Bashkiria.