Universal Jensen's Equations in Banach Modules over a C-Algebra and Its Unitary Group

In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C~*-algebra.Moreover,we prove the stability of linear operators in a Hilbert module over a unitat C~*-algebra.

Estimation of soil erosion risk within a small mountainous sub-watershed in Kerala,India,using Revised Universal Soil Loss Equation(RUSLE) and geo-information technology

A comprehensive methodology that integrates Revised Universal Soil Loss Equation （RUSLE） model and Geographic Information System （GIS） techniques was adopted to determine the soil erosion vulner- ability of a forested mountainous sub-watershed in Kerala, India. The spatial pattern of annual soil erosion rate was obtained by integrating geo-environmental variables in a raster based GIS method. GIS data layers including, rainfall erosivity （R）, soil erodability （K）, slope length and steepness （LS）, cover management （C） and conservation practice （P） factors were computed to determine their effects on average annual soil loss in the area. The resultant map of annual soil erosion shows a maximum soil loss of 17.73 t h-1 y i with a close relation to grass land areas, degraded forests and deciduous forests on the steep side-slopes （with high LS ）. The spatial erosion maps generated with RUSLE method and GIS can serve as effective inputs in deriving strategies for land planning and management in the environmentally sensitive mountainous areas.

Integrated Approach of Universal Soil Loss Equation (USLE) and Geographical Information System (GIS) for Soil Loss Risk Assessment in Upper South Koel Basin, Jharkhand

Soil erosion is a growing problem especially in areas of agricultural activity where soil erosion not only leads to decreased agricultural productivity but also reduces water availability. Universal Soil Loss Equation (USLE) is the most popular empirically based model used globally for erosion prediction and control. Remote sensing and GIS techniques have become valuable tools specially when assessing erosion at larger scales due to the amount of data needed and the greater area coverage. The present study area is a part of Chotanagpur plateau with undulating topography, with a very high risk of soil erosion. In the present study an attempt has been made to assess the annual soil loss in Upper South Koel basin using Universal Soil Loss Equation (USLE) in GIS framework. Such information can be of immense help in identifying priority areas for implementation of erosion control measures. The soil erosion rate was determined as a function of land topography, soil texture, land use/land cover, rainfall erosivity, and crop management and practice in the watershed using the Universal Soil Loss Equation (for Indian conditions), remote sensing imagery, and GIS techniques. The rainfall erosivity R-factor of USLE was found as 546 MJ mm/ha/hr/yr and the soil erodibility K-factor varied from 0.23 - 0.37. Slopes in the catchment varied between 0% and 42% having LS factor values ranging from 0 - 21. The C factor was computed from NDVI (Normalized Difference Vegetative Index) values derived from Landsat-TM data. The P value was computed from existing cropping patterns in the catchment. The annual soil loss estimated in the watershed using USLE is 12.2 ton/ha/yr.

Evaluation of C and P Factors in Universal Soil Loss Equation on Trapping Sediment: Case Study of Santubong River

Universal Soil Loss Equation (USLE) is the most comprehensive technique available to predict the long term average annual rate of erosion on a field slope. USLE was governed by five factors include soil erodibility factor (K), rainfall and runoff erodibility index (R), crop/vegetation and management factor (C), support practice factor (P) and slope length-gradient factor (LS). In the past, K, R and LS factors are extensively studied. But the impacts of factors C and P to outfall Total Suspended Solid (TSS) and % reduction of TSS are not fully studied yet. Therefore, this study employs Buffer Zone Calculator as a tool to determine the sediment removal efficiency for different C and P factors. The selected study areas are Santubong River, Kuching, Sarawak. Results show that the outfall TSS is increasing with the increase of C values. The most effective and efficient land use for reducing TSS among 17 land uses investigated is found to be forest with undergrowth, followed by mixed dipt. forest, forest with no undergrowth, cultivated grass, logging 30, logging 10^6, wet rice, new shifting agriculture, oil palm, rubber, cocoa, coffee, tea and lastly settlement/cleared land. Besides, results also indicate that the % reduction of TSS is increasing with the decrease of P factor. The most effective support practice to reduce the outfall TSS is found to be terracing, followed by contour-strip cropping, contouring and lastly not implementing any soil conservation practice.

Factor value determination and applicability evaluation of universal soil loss equation in granite gneiss region

Six types of runoff plots were set up and an experimental study was carried out to examine natural rate of soil and water loss in the granite gneiss region of northern Jiangsu Province in China. Through correlation analysis of runoff and soil loss during 364 rainfall events, a simplified and convenient mathematical formula suitable for calculating the rainfall erosivity factor （R） for the local region was established. Other factors of the universal soil loss equation （USLE model） were also determined. Relative error analysis of the soil loss of various plots calculated by the USLE model on the basis of the observed values showed that the relative error ranged from -3.5% to 9.9% and the confidence level was more than 90%. In addition, the relative error was 5.64% for the terraced field and 12.36% for the sloping field in the practical application. Thus, the confidence level was above 87.64%. These results provide a scientific basis for forecasting and monitoring soil and water loss, for comprehensive management of small watersheds, and for soil and water conservation planning in the region.

A Survey Study on TPACK Framework for Normal Students of English Major in Ethnic Colleges and Universities:Empirical Analysis Based on Structural Equation Modeling

With the continuous advancement of education informatization,Technological Pedagogical Content Knowledge(TPACK),as a new theoretical framework,provides a novel method for measuring teachers’informatization teaching ability.This study takes normal students of English majors from three ethnic universities as the research object,collects relevant data through questionnaires,and uses structural equation modeling to conduct data analysis and empirical research to investigate the differences in the TPACK levels of these students at different grades and the structural relationships among the elements in the TPACK structure.The technological pedagogical knowledge element of the TPACK structure was not obtained by exploratory factors analysis but through path analysis and structural equation modeling,the results show that the one-dimensional core knowledge of technological knowledge(TK),content knowledge(CK),and pedagogical knowledge(PK)have a positive effect on the two-dimensional interaction knowledge of technological content knowledge(TCK)and pedagogical content knowledge(PCK);furthermore,TCK and PCK have a positive effect on TPACK;and TK,CK,and PK indirectly affect TPACK through TCK and PCK.On this basis,suggestions are provided to ethnic colleges and universities to develop the TPACK knowledge competence of normal students of English majors.

A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

Continued Fraction Evaluation of the Universal Y’s Functions

In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic).

Emergence of Friedmann Equation of Cosmology of a Flat Universe from the Time-Energy Uncertainty Principle

Friedmann equation of cosmology is based on the field equations of general relativity. Its derivation is straight-forward once the Einstein’s field equations are given and the derivation is independent of quantum mechanics. In this paper, it is shown that the Friedmann equation pertinent to a homogeneous, isotropic and flat universe can also be obtained as a consequence of the energy balance in the expanding universe between the positive energy associated with vacuum and matter, and the negative gravitational energy. The results obtained here is a clear consequence of the fact that the surface area of the Hubble sphere is proportional to the total amount of information contained within it.

A New Solution for the Friedmann Equations

Assuming a flat universe expanding under a constant pressure and combining the first and the second Friedmann equations, a new equation, describing the evolution of the scale factor, is derived. The equation is a general kinematic equation. It includes all the ingredients composing the universe. An exact closed form solution for this equation is presented. The solution shows remarkable agreement with available observational data for redshifts from a low of z = 0.0152 to as high as z = 8.68. As such, this solution provides an alternative way of describing the expansion of space without involving the controversial dark energy.

SOME DYNAMICAL BEHAVIOR OF THE STUART-LANDAU EQUATION WITH A PERIODIC EXCITATION

The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency are investigated in detail, respectively.The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.

TENSOR UNIVERSAL SERENDIPITY ELEMENTS AND UNSTEADY TAYLOR-GALERKIN FINITE ELEMENT METHOD

A new kind of Universal Serendipity Element (USE) - the Tensor Universal Serendipity Element (TUSE) is constructed by using both tensor force finite elements and the basic idea of USE. The formulation of shape functions and their derivatives for TUSE is presented. TUSE can be used to study steady and unsteady transonic flow fields when combined with Taylor-Galerkin Finite Element Methods, the NND scheme in FDM, and four-stage Runge-Kutta methods. As numerical examples the transonic flow in cascades and one kind of complex unsteady transonic axisymmetric how in engineering are studied. It is shown that the algorithm presented in this paper is efficient and robust.

TO SOLVE MATRIX EQUATION sum (A^iXBi=c) BY THE SMITH NORMAL FORM

By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.

ANOTHER CLASS D＇ALEMBERT PRINCIPLE AND A NEW MAGGI EQUATION FOR ARBITRARY ORDER NONHOLONOMIC MECHANICAL SYSTEMS IN DERIVATIVE SPACE

As a concrete application of the concepts of 'derivative space' and'correspondent kinetic energy' in derivative space, and of foe thought of 'treatingnonholonomic systems by changing them into formal holonomic system' which theauthors have previously proposed in references [1. 2, 3]. this paper derived another newuniversal D'Alembert principle and a new Maggi equation for arbitrary ordernonholonomic mechanical systems. An example using the Maggi equation is given.

Relationship between drought and soil erosion based on the normalized differential water index(NDWI)and revised universal soil loss equation(RUSLE)model

The Langat River Basin in Malaysia is vulnerable to soil erosion risks because of its exposure to intensive land use activities and its topography,which primarily consists of steep slopes and mountainous areas.Furthermore,climate change frequently exposes this basin to drought,which negatively affects soil and water conservation.However,recent studies have rarely shown how soil reacts to drought,such as soil erosion.Therefore,the purpose of this study is to evaluate the relationship between drought and soil erosion in the Langat River Basin.We analyzed drought indices using Landsat 8 satellite images in November 2021,and created the normalized differential water index(NDWI)via Landsat 8 data to produce a drought map.We used the revised universal soil loss equation(RUSLE)model to predict soil erosion.We verified an association between the NDWI and soil erosion data using a correlation analysis.The results revealed that the southern and northern regions of the study area experienced drought events.We predicted an average annual soil erosion of approximately 58.11 t/(hm^(2)·a).Analysis of the association between the NDWI and soil erosion revealed a strong positive correlation,with a Pearson correlation coefficient of 0.86.We assumed that the slope length and steepness factor was the primary contributor to soil erosion in the study area.As a result,these findings can help authorities plan effective measures to reduce the impacts of drought and soil erosion in the future.

A New Wave Equation of the Electron

A new form of Dirac equation of a second order partial differential equation is found. With this wave equation the quivering motion (Zitterbewegung) is satisfactorily explained. A quaternionic analogue of Dirac equation is presented and compared with the ordinary Dirac equation. The two equations become the same if we replace the particle rest mass, m0, in the latter by im0. New space and time transformations in which these two equations represent a massless particle are found. The invariance of Klein-Gordon equation under these transformations yields the Dirac equation. The electron is found to be represented by a superposition of two waves with a group velocity equals to speed of light in vacuum.

A Solution of Kepler’s Equation

The present study deals with a traditional physical problem: the solution of the Kepler’s equation for all conics (ellipse, hyperbola or parabola). Solution of the universal Kepler’s equation in closed form is obtained with the help of the two-dimensional Laplace technique, expressing the universal functions as a function of the universal anomaly and the time. Combining these new expressions of the universal functions and their identities, we establish one biquadratic equation for universal anomaly (χ) for all conics;solving this new equation, we have a new exact solution of the present problem for the universal anomaly as a function of the time. The verifying of the universal Kepler’s equation and the traditional forms of Kepler’s equation from this new solution are discussed. The plots of the elliptic, hyperbolic or parabolic Keplerian orbits are also given, using this new solution.

The Jeans Equation Generalization for the Rotating Universe

The generalization of Jeans equation in expanding and rotating Universe is given. We found the generalized frequency of baryonic substrate oscillations in the rotating Universe. In doing this, two cases were considered: the generalized wave vector coincides with the Jeans wave vector and second case, when the generalized wave vector tends to zero.

Investigating Initial Conditions of the WdW Equation in Flat Space in a Transition from the Pre-Planckian Physics Era to the Electroweak Regime of Space-Time

This document is due to reviewing an article by Maydanyuk and Olkhovsky, of a Nova Science conpendium as of “The big bang, theory assumptions and Problems”, as of 2012, which uses the Wheeler De Witt equation as an evolution equation assuming a closed universe. Having the value of k, not as the closed universe, but nearly zero of a nearly flat universe, which leads to serious problems of interpretation of what initial conditions are. These problems of interpretations of initial conditions tie in with difficulties in using QM as an initial driver of inflation. And argue in favor of using a different procedure as far as forming a wave function of the universe initially. The author wishes to thank Abhay Ashtekar for his well thought out criticism but asserts that limitations in space-time geometry largely due to when is formed from semi classical reasoning, i.e. Maxwell’s equation involving a close boundary value regime between Octonionic geometry and flat space non Octonionic geometry is a datum which Abhay Ashekhar may wish to consider in his quantum bounce model and in loop quantum gravity in the future.

Revised Newtonian Formula of Gravity and Equation of Cosmology in Flat Space-Time Transformed from Schwarzschild Solution

By transforming the geodesic equation of the Schwarzschild solution of the Einstein’s equation of gravity field to flat space-time for description, the revised Newtonian formula of gravity is obtained. The formula can also describe the motion of object with mass in gravity field such as the perihelion precession of the Mercury. The space-time singularity in the Einstein’s theory of gravity becomes the original point r = 0 in the Newtonian formula of gravity. The singularity problem of gravity in curved space-time is eliminated thoroughly. When the formula is used to describe the expansive universe, the revised Friedmann equation of cosmology is obtained. Based on it, the high red-shift of Ia supernova can be explained well. We do not need the hypotheses of the universe accelerating expansion and dark energy again. It is also unnecessary for us to assume that non-baryon dark material is 5 - 6 times more than normal baryon material in the universe if they really exist. The problem of the universal age can also be solved well. The theory of gravity returns to the traditional form of dynamic description and becomes normal one. The revised equation can be taken as the foundation of more rational cosmology.