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Bilaterally Symmetrical Transformation between Independent Operators and rotations

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Journal of Quantum Information Science 2015年第3期5卷 79-88页

作者： Nikolay Raychev Department of Computer Systems Varna University of Management Varna Bulgaria

This report describes an approach for representation of quantum operators through rotations and rotation through quantum operators. The approach of the proposed method transforms rotation in a kind of a unitary matrix that corresponds to the rotation. Operations with qubits are very similar to the rotation, but with an added phase coefficient. This fact is used to create a process for rotation between unitary matrices. This approach could be used to modifying the controls to apply in a different basis.

关键词： Quantum Operators rotations Phase Space Quantum Circuit

Cereal-forage crop rotations and irrigation treatment effect on water use efficiency and crops sustainability in Mediterranean environment

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Agricultural Sciences 2012年第1期3卷 44-57页

作者： Pasquale Martiniello Agricultural Research Council Unit for Extensive Animal Production Muro Lucano (Potenza) Italy

Agricultural systems based on crop rotations favour sustainability of cultivation and productivity of the crops. Wheat-forage crops rotations (annual winter binary mixture and perennial alfalfa meadow) combined with irrigation are the agronomical techniques able to better exploit the weather resources in Mediterranean environments. The experiment aimed to study the effect of 18 years of combined effect of irrigation and continuous durum wheat and wheat-forage rotations on productivities of crops and organic matter of topsoil. The experiments were established through 1991-2008 under rainfed and irrigated treatments and emphasized on the effect of irrigation and continuous wheat and wheat-forage crop rotations on water use efficiency and sustainability of organic matter. The effect of irrigation increased 49.1% and 66.9% the dry matter of mixture and meadow, respectively. Continuous wheat rotation reduced seed yield, stability of production, crude protein characteristics of kernel and soil organic matter. The yearly gain in wheat after forage crops was 0.04 t (ha·yr)-1 under rainfed and 0.07 t (ha·yr)-1 under irrigation treatments. The crude protein and soil organic matter of wheat rotations, compared to those of continuous wheat under rainfed and irrigated was increase in term of point percentage by 0.8 and 0.5 in crude protein and 5.1 and 4.4 in organic matter, respectively. The rotations of mixture and meadow under both irrigated treatments increased the point of percentage of organic matter over continuous wheat (*** 8.5 in mixture and 12.5 and 9.5 meadow under rainfed and irrigation, respectively). Irrigation reduce the impact of weather on crop growing reducing water use efficiency (mean over rotations) for dry mater production (15.5 in meadow and 17.5 in mixture [L water (kg·dry·matter)-1 ]) and wheat seed yield. The effect of agronomic advantages achieved by forage crops in topsoil expire its effect after three years of continuous wheat rotation.

关键词： Alfalfa Binary Mixture Durum Wheat Irrigation Mediterranean Environment Soil Organic Matter Water Use Efficiency Wheat-Forage rotations

New Method of Givens rotations for Triangularization of Square Matrices

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Advances in Linear Algebra & Matrix Theory 2014年第2期4卷 65-78页

作者： Artyom M. Grigoryan Department of Electrical and Computer Engineering The University of Texas at San Antonio San Antonio USA

This paper describes a new method of QR-decomposition of square nonsingular matrices (real or complex) by the Givens rotations through the unitary discrete heap transforms. This transforms can be defined by a different path, or the order of processing components of input data, which leads to different realizations of the QR-decomposition. The heap transforms are fast, because of a simple form of decomposition of their matrices. The direct calculation of the N-point discrete heap transform requires no more than 5(N-1) multiplications, 2(N-1) additions, plus 3(N-1) trigonometric operations. The QR-decomposition of the square matrix N × N uses about 4/3N3 multiplications and N(N-1)/2 square roots. This number varies depending on the path of the heap transform, and it is shown that “the optimal path” allows for significant reduction of number of operations in QR-decomposition. The heap transform and its matrix can be described analytically, and therefore, this transform can also be applied to the QR-decomposition of complex matrices.

关键词： QR-Factorization Givens rotations Householder Reflections Heap Transform

Persistence in tillage decisions: Aggregate data analysis

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International Soil and Water Conservation Research 2019年第2期7卷 109-118页

作者： Dat Q.Tran Lyubov A.Kurkalova University of Arkansas at Fayetteville AR 72701Department of Agricultural Economics and AgribusinessUSA Can Tho University Department of Hydraulic EngineeringVietnam 1601 E.Market St. GreensboroNC27411North Carolina A&T State UniversityDepartment of EconomicsUSA 1601 E.Market St. GreensboroNC27411North Carolina A&T State UniversityDepartment of Energy and Environmental SystemsUSA

The Emission Gap Report 2013 from the United Nations Environment Program showed that adopting conservation tillage such as no-till,as an alternative to conventional tillage,contributes significantly to climate change mitigation through carbon ***,substantial amounts of soil carbon are lost when farmers interrupt continuous use of conservation tillage with conventional *** tillage is spreading,but little is known about the behavioral persistence in tillage *** address the gap in the literature,we estimate county-specific Markov models of tillage-crop choices,and use the predicted probabilities of alternative two-and three-year tillage rotations to evaluate spatial variation and temporal persistence in conservation tillage adoption for the state of lowa (U.S).We find that the county-average probabilities of continuous conservation tillage range between 0.133 and 0.295,and vary significantly among crop *** also find a statistically strong positive effect of the incidence of the highly erodible land on the county-average use of continuous conservation *** results underscore the importance of dynamic modeling for understanding behavioral persistence in tillage decisions,and the interdependence between farmers' crop and tillage rotations.

关键词： Aggregate data Continuous conservation tillage Markov chain model Crop rotations Highly erodible land

SSA-HIAST: A Novel Framework for Code Clone Detection

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Computers, Materials & Continua 2022年第5期71卷 2999-3017页

作者： Neha Saini Sukhdip Singh Deenbandhu Chhotu Ram University of Science and Technology Murthal131001India

In the recent era of software development,reusing software is one of the major activities that is widely used to save *** reuse software,the copy and paste method is used and this whole process is known as code *** activity leads to problems like difficulty in debugging,increase in time to debug and manage software *** the literature,various algorithms have been developed to find out the clones but it takes too much time as well as more space to figure out the ***,most of them are not *** problem has been targeted upon in this *** the proposed framework,authors have proposed a new method of identifying clones that takes lesser time to find out clones as compared with many popular code clone detection *** proposed framework has also addressed one of the key issues in code clone detection i.e.,detection of near-miss(Type-3)and semantic clones(Type-4)with significant accuracy of 95.52%and 92.80%*** present study is divided into two phases,the first method converts any code into an intermediate representation form i.e.,Hashinspired abstract syntax *** the second phase,these abstract syntax trees are passed to a novel approach“Similarity-based self-adjusting hash inspired abstract syntax tree”algorithm that helps in knowing the similarity level of *** proposed method has shown a lot of improvement over the existing code clones identification methods.

关键词： Code cloning clone detection hash inspired abstract syntax tree rotations hybrid framework

On the Rotation of a Vector Field in a Four-Dimensional Space

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Applied Mathematics 2014年第1期5卷 128-136页

作者： Leonardo Simal Moreira UniFOA—Centro Universitário de Volta Redonda Volta Redonda Brazil

Recently I published a paper in the journal ALAMT (Advances in Linear Algebra & Matrix Theory) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to this work, it is proposed to develop, through dimensional analogy, a vector field with notation and properties analogous to the curl, in this case applied to the space IR4. One can see how the similarities are obvious in relation to the algebraic properties and the geometric structures, if the rotations are compared in spaces of three and four dimensions.

关键词： Products of Vectors Dimensional Analogy Vector Fields Curl rotations Curl by Analogy

Formalized Operators with Phase Encoding

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Journal of Quantum Information Science 2015年第3期5卷 114-126页

作者： Nikolay Raychev School of Computing Varna University of Management Varna Bulgaria

In this article the concept of phase encoding/decoding is used to analyze and formalize a simple quantum algorithm—the Deutsch’s algorithm. The algorithm is formalized in two different ways through an analysis, based on phase encoding/decoding, carried out by the formalized elementary operators developed by the author of this article. Concrete examples of different possible realizations of the formalized with Raychev’s operators Deutsch’s algorithms are offered.

关键词： Quantum Operators rotations Phasespace Quantum Circuit

Finite Element Processes Based on GM/WF in Non-Classical Solid Mechanics

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American Journal of Computational Mathematics 2017年第3期7卷 321-349页

作者： K. S. Surana R. Shanbhag J. N. Reddy Department of Mechanical Engineering University of Kansas Lawrence KS USA Department of Mechanical Engineering Texas A & M University College Station TX USA

In non-classical thermoelastic solids incorporating internal rotation and conjugate Cauchy moment tensor the mechanical deformation is reversible. This suggests that within the realm of linear mathematical models that only consider small strains and small deformation the mechanical deformation is reversible. Hence, it is possible to recast the conservation and balance laws along with constitutive theories in a form that adjoint A* of the differential operator A in mathematical model is same as the differential operator A. This holds regardless of whether we consider an initial value problem (IVP) (when the integrals over open boundary are neglected) or boundary value problem (BVP). Thus, in such cases Galerkin method with weak form (GM/WF) for BVPs and space-time Galerkin method with weak form (STGM/WF) for IVPs are highly meritorious due to the fact that: 1) the integral form for BVPs is variationally consistent (VC) and 2) the space-time integral forms for IVP are space time variationally consistent (STVC). The consequence of VC and STVC integral forms is that the resulting coefficient matrices are symmetric and positive definite ensuring unconditionally stable computational processes for both BVPs and IVPs. Other benefits of GM/WF and space-time GM/WF are simplicity of specifying boundary conditions and initial conditions, especially traction boundary conditions and initial conditions on curved boundaries due to self-equilibrating nature of the sum of secondary variables that only exist in GM/WF due to concomitant. In fact, zero traction conditions are automatically satisfied in GM/WF, hence need not be specified at all. While VC and STVC feature also exists in least squares process (LSP) and space-time least squares finite element processes (STLSP) for BVPs and IVPs, the ease of specifying traction boundary conditions feature in GM/WF and STGM/WF is highly meritorious compared to LSP and STLSP in which zero traction conditions need to be explicitly specified. A

关键词： Non-Classical Continua Polar Continua Lagrangian Description Internal rotations Galerkin Method with Weak Form

Continued Fractions and Dynamics

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Applied Mathematics 2014年第7期5卷 1067-1090页

作者： Stefano Isola Dipartimento di Matematica e Informatica Università degli Studi di Camerino Camerino Macerata Italy

Several links between continued fractions and classical and less classical constructions in dynamical systems theory are presented and discussed.

关键词： Continued Fractions Fast and Slow Convergents Irrational rotations Farey and Gauss Maps Transfer Operator Thermodynamic Formalism