Linear Form Research Articles

On a Linear Form in the Ordinates of Zeros of the Riemann Zeta Function

В работе получена асимптотическая формула для суммы $$ H=\sum_{0<\gamma_k\leqslant T, 1\leqslant k\leqslant 4}h(\gamma_1+\gamma_2-\gamma_3-\gamma_4), $$ где $\gamma_k$ пробегают мнимые части нетривиальных нулей дзета-функции Римана с учетом кратности, а функция $h$ принадлежит некоторому специальному классу функций из $L^1(\mathbb R)$. Библиография: 7 названий.

Numerical modeling of cutting force and chip formation during water Jet Assisted Machining of Ti17 based on SPH/FEM method

In this paper, we conduct a numerical simulation of a water jet-assisted machining process for a titanium alloy Ti17, with a focus on addressing the Fluid-Structure Interaction (FSI) problem arising during lubricated machining. The proposed coupling strategy employs the Smoothed Particle Hydrodynamics (SPH) free mesh method, coupled with an ordinary Lagrangian mesh. The SPH method is utilized to model the water jet, while the Lagrangian Finite Element Method (FEM) is employed to represent the workpiece and the tool. The hydrodynamic behavior of water is captured using the linear Huguenot form of the Mie-Greisen equation of state. Additionally, the Johnson-Cook constitutive law is applied to describe the thermoviscoplastic behavior of the titanium alloy. It is essential to note that thermal and mechanical effects were decoupled in this study. The investigation focuses on cutting force and chip morphology under two distinct cutting regimes: Dry Machining (DM) and Water Jet Assisted Machining, specifically with conventional lubrication (CL). The numerical simulations are compared with experimental results found in the literature, with an emphasis on cutting force and chip morphology. The obtained simulation results exhibit a favorable correlation with the experimental data. All numerical simulations were conducted using ABAQUS version 6.14.

Optimization Models for Long-Term Planning of Municipal Solid Waste Management Systems: A Review with An Emphasis on Mass Balances

The vast majority of decision-making approaches used for long-term planning of municipal solid waste management systems (LPMSWMS) are ground on scenario-based structures. However, the scenario-based structures may overlook many real-world possibilities because of their restricted mass balances. This study is the first attempt to review the current state of optimization models, which are used as a decision-making approach for LPMSWMS, by focusing on the mass balances. In line with this purpose, 146 peer-reviewed articles were examined based on a new literature evaluation scheme. According to the findings, it can be stated that a significant majority of the articles offer non-deterministic optimization models dealing with the uncertain nature of the LPMSWMS problems. Considering all optimization models examined in the study, most of the model formulations have linear mathematical forms in terms of objective and constraint functions. However, it is quite interesting that none of the models produced solutions for a management system alternative with an integrated (non-restricted) mass balance. Accordingly, it is very questionable whether the results obtained from the current models have the power to give the most suitable solution for an up-to-date management system. As a result of the review, it is highly recommended that the optimization models to be conducted for the LPMSWMS in the future should search for new mathematical approaches considering the integrated mass balances under certainty and/or uncertainty.

Constrained mean-variance investment-reinsurance under the Cramér–Lundberg model with random coefficients

In this paper, we study an optimal mean-variance investment-reinsurance problem for an insurer (she) under the Cramér–Lundberg model with random coefficients. At any time, the insurer can purchase reinsurance or acquire new business and invest her surplus in a security market consisting of a risk-free asset and multiple risky assets, subject to a general convex cone investment constraint. We reduce the problem to a constrained stochastic linear-quadratic control problem with jumps whose solution is related to a system of partially coupled stochastic Riccati equations (SREs). Then we devote ourselves to establishing the existence and uniqueness of solutions to the SREs by pure backward stochastic differential equation (BSDE) techniques. We achieve this with the help of approximation procedure, comparison theorems for BSDEs with jumps, log transformation and BMO martingales. The efficient investment-reinsurance strategy and efficient mean-variance frontier are explicitly given through the solutions of the SREs, which are shown to be a linear feedback form of the wealth process and a half-line, respectively.

Look-Ahead Rolling Economic Dispatch Approach for Wind-Thermal-Bundled Power System Considering Dynamic Ramping and Flexible Load Transfer Strategy

With a wind-thermal-bundled power system (WTBPS) under high wind penetration levels, the sharp power fluctuations of tie-lines for interconnected grids trigger a significant challenge of security-constrained power system operation. Smoothing power fluctuations with economic dispatch is widely concerned against this challenge. In this paper, an appropriate look-ahead economic dispatch framework for WTBPS considering the variable ramp rate of retrofitted coal-fired units and the flexible load transfer strategy (LTS) in high voltage distribution networks (HVDNs) is proposed. To cope with this issue, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) we derive a new family of tightened ramping constraints of retrofitted coal-fired units in the linear and second-order conic (SOC) forms, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) Using graph characterization of typical HVDNs, the simplified voltage-constrained LTS via topological structures can be developed. This proposed look-ahead economic dispatch model is cast as a mixed-integer second-order cone programming (MISOCP) problem, which can be reformulated by Multi-cut Generalized Benders Decomposition (MGBD). This MGBD enables multiple sub-problems can be solved in parallel and accelerates the solving process. Finally, simulation results of a large-scale practical system validate the computational accuracy and efficiency of the proposed approach.

Natural frequencies of bars with variable cross-sections

This paper presents the possibility of determining the natural frequency of flexural bars treated as Bernoulli-Euler beams using the Rayleigh method. It is assumed that the shape of the bar axis during vibration is the same as the shape of the deflection line of this bar under continuous load. By comparing the potential energy in the deflected position with the kinetic energy in the undeflected position, it is possible to determine the frequency and period of natural vibration as a function of Young's modulus and material density, as well as the parameters describing the geometric shape of the bar. Examples of solutions for truncated cone and truncated wedge-shaped bars are shown, as well as a solids of revolution with the generatrix described by linear and curvilinear (parabolic, exponential) forms. It applies to both solid and hollow bars, and different types of fixing the ends of the bar. The accuracy of the obtained results (compared with the literature and with the results of FEM calculations) is sufficient for practical applications. The authors also showed the possibility of extending the method to higher frequencies of vibration.

Multi-Stage Decision Rules for Power Generation &amp; Storage Investments With Performance Guarantees

We develop multi-stage linear decision rules (LDRs) for dynamic power system generation and energy storage investment planning under uncertainty and propose their chance-constrained optimization with performance guarantees. First, the optimized LDRs guarantee operational and carbon policy feasibility of the resulting dynamic investment plan even when the planning uncertainty distribution is ambiguous. Second, the optimized LDRs internalize the tolerance of the system planner towards the stochasticity (variance) of uncertain investment outcomes. They can eventually produce a quasi-deterministic investment plan, which is insensitive to uncertainty (as in deterministic planning) but robust to its realizations (as in stochastic planning). Last, we certify the performance of the optimized LDRs with the bound on their sub-optimality due to their linear functional form. Using this bound, we guarantee that the preference of LDRs over less restrictive – yet poorly scalable – scenario-based optimization does not lead to financial losses exceeding this bound. We use a testbed of the U.S. Southeast power system to reveal the trade-offs between the cost, stochasticity, and feasibility of LDR-based investments. We also conclude that the LDR sub-optimality depends on the amount of uncertainty and the tightness of chance constraints on operational, investment and policy variables.

ON THE OPTIMAL DISCRETIZATION OF THE SOLUTIONPOISSON’S EQUATION

The paper studies the problem of discretizing the solution of the Poisson equation with the right hand side f belonging to the multidimensional periodic Sobolev class. The research methodology is based on considering the problem of discretizing the solution of the Poisson equation as one of the concretizations of the general problem of optimal recovery of the operator Tf and using well known statements of approximation theory. Within the framework of this general optimal recovery problem, we first estimate from above the smallest discretization error N of the solution of the Poisson equation in the Hilbert metric using the discretization operator (l(N) , N) constructed from a finite set of Fourier coefficients of the function f. A lower estimate, coinciding in order with the upper estimate, for the smallest error N was obtained by involving all linear functionals defined on the multidimensional Sobolev class. It should be noted that the optimal discretization operator (l(N) , N) better approximates the solution under consideration in the Hilbert metric than any discretization operator constructed from values f at given points. Poisson’s equation is an elliptic partial differential equation and describes many physical phenomena such as electrostatic field, stationary temperature field, pressure field and velocity potential field in hydrodynamics. Therefore, the relevance of the research conducted here is beyond doubt.

Distributional Boundary Values of Analytic Functions

Let D be a connected bounded domain in R2, S be its boundary which is closed, connected and smooth. Let Φ(z) = 1 2πi R S ϕ(s)ds s−z , ϕ ∈ X, z = x + iy, X is a Banach space of linear bounded functionals on Hμ, a Banach space of distributions, and Hμ is the Banach space of Hoelder-continuous functions on S with the usual norm. As X one can use also the space Hoelder continuous of bounded linear functionals on the Sobolev space Hℓ on S. Distributional boundary values of Φ(z) on S are studied in detail. The function Φ(t), t ∈ S, is defined in a new way. Necessary and sufficient conditions are given for ϕ ∈ X to be a boundary value of an analytic in D function. The Cauchy formula is generalized to the case when the boundary values of an analytic function in D are tempered distributions. The Sokhotsky-Plemelj formulas are derived for ϕ ∈ X.

A new characterization of the dual space of the HK-integrable functions

&lt;abstract&gt;&lt;p&gt;We construct the Henstock-Kurzweil (HK) integral as an extension of a linear form initially defined on $ L^{1} $, but which is not continuous in this space. This gives us an alternative way to prove existing results. In particular, we give a new characterization of the dual space of Henstock-Kurzweil integrable functions in terms of a quotient space.&lt;/p&gt;&lt;/abstract&gt;

Research of direct and inverse problems of sensitivity using methods of practical stability by direction

The general statements of the problems of construction of extreme ranges of tolerances on parameters for a linear system of differential equations in the presence of dynamic restrictions on the spread of the state vector are considered. It was found that such sensitivity problems are closely related to the problems of estimating the maximum area of stability in the corresponding function space. In order to obtain upper estimates of the sought values, the problem of estimating tolerances from the positions of stability in a single direction is formalized. The cases of linear and nonlinear restrictions on the spread of the phase coordinate vector with initial linear initial conditions relative to the vector of the system parameters are studied. Necessary and sufficient conditions are formulated in the form of criteria for estimating tolerances on parameters covering the case of fixed initial conditions. The tasks of estimating the maximum volume of the stability region with respect to the deviations of the state vectors and system parameters are considered. For the case of compatible admissible constraints, the paper gives the corresponding numerical calculations for the upper estimates. In particular, for fixed initial conditions, the maximum set of tolerances for system parameters with compatible dynamic restrictions on fluctuations of state vectors and parameters are determined according to these evaluation criteria. From the standpoint of practical stability in direction, direct sensitivity problems are investigated, numerical estimates of the spread of the phase coordinate vector of the system in the presence of linear and fixed initial conditions relative to the parameter vector are given. It has been demonstrated that in the given specification of the problem of maximum estimation of tolerances it is completely covered by problem statements of practical stability by direction. Thus, to calculate areas of guaranteed sensitivity, the concept of practical stability in a single direction is extended to the space of sensitivity functions at the initial moment of time. The above algorithms are used to estimate the range of tolerances for the adjustment parameters of the discrete model of the induction acceleration system with the given limitations on the spread of the quality criterion; the variation of the quality indicator within the tolerance field is presented in the form of a linear form relative to the spread of the parameter vector.

Metrical results on the geometry of best approximations for a linear form, I

Metrical results on the geometry of best approximations for a linear form, I

Рациональные коэффициенты ортогональных разложений некоторых функций

Expansions of many elementary and special functions in series of orthogonal polynomials have coefficients known explicitly. However, almost always these coefficients are irrational. Thus any numerical method would give these coefficients approximately with computations in any arithmetic. This is also true for the spectral methods, which give effective approximations for holonomic functions. However, in some exceptional cases the coefficients of expansions obtained with spectral methods turn out to be rational, and are computed exactly in rational arithmetic. We consider these expansions in series of some classical orthogonal polynomials. We demonstrate that, in this way, an infinite number of linear forms can be obtained for some irrationalities, in particular, for the Euler constant.

Small molecule interactions with biomacromolecules: selective sensing of human serum albumin by a hexanuclear manganese complex - photophysical and biological studies.

A covalently bonded hexanuclear neutral complex, [Mn6(μ3-O)2(3-MeO-salox)6(OAc)2(H2O)4] (1), has been synthesized and characterized by single crystal X-ray diffraction analysis along with IR and HRMS studies. Complex 1 has been found to selectively interact with human serum albumin (HSA), a model transport protein. The interaction of 1 with HSA was investigated by monitoring the change in the absorbance value of HSA at λ = 280 nm with increasing concentration of 1. Likewise, fluorescence titrations were carried out under two conditions: (i) titration of a 5 μM solution of complex 1 with the gradual addition of HSA, showing a ∼9-fold fluorescence intensity enhancement at 424 nm, upon excitation at 300 nm; and (ii) upon excitation at 295 nm, titration of 5 μM HSA solution with the incremental addition of complex 1, showing a quenching of fluorescence intensity at 334 nm, with simultaneous development of a new emission band at 424 nm. A linear form of the Stern-Volmer equation gives KSV = 9.77 × 104 M-1 and the Benesi-Hildebrand plot yields the binding constant as KBH = 1.98 × 105 M-1 at 298 K. The thermodynamic parameters, ΔS°, ΔH°, and ΔG°, were estimated by using the van't Hoff relationship which infer the major contribution of hydrophobic interactions between HSA and 1. It was observed that quenching of HSA emission arises mainly through a dynamic quenching mechanism as indicated by the dependence of average lifetime 〈τ〉 on the concentration of 1. The changes in the CD (circular dichroism) spectral pattern of HSA in the presence of 1 clearly establish the variation of HSA secondary structure on interaction with 1. The most probable interaction region in HSA for 1 was determined from molecular docking studies which establish the preferential trapping of 1 in the subdomain IIA of site I in HSA and substantiated by the results of site-specific marker studies. Complex 1 was further evaluated for its antiproliferative effects in lung cancer A549 cells, which strictly inhibits the growth of the cells in both 2D and 3D mammospheres, indicating its potential application as an anticancer drug.

Repdigits base $ \eta $ as sum or product of Perrin and Padovan numbers

&lt;abstract&gt;&lt;p&gt;Let $ \left\{E_{n}\right\}_{n\geq0} $ and $ \left\{P_{n}\right\}_{n\geq0} $ be sequences of Perrin and Padovan numbers, respectively. We have found all repdigits that can be written as the sum or product of $ E_{n} $ and $ P_{m} $ in the base $ \eta $, where $ 2\leq\eta\leq10 $ and $ m\leq n $. In addition, we have applied the theory of linear forms in logarithms of algebraic numbers and Baker-Davenport reduction method in Diophantine approximation approaches.&lt;/p&gt;&lt;/abstract&gt;

Length-Weight Relationship of Fishes in Some Rivers of Morang, Nepal

The length-weight relationship is a crucial aspect of fishery assessments, providing valuable biological information. The length-weight relationship is expressed by the equation W = aLb, where W represents the total weight of the fish and L denotes the standard length. The LWR equation was transformed into a linear form using logarithmic transformation: LogW = a + bLogL. The biometric data obtained from this study includes information on species, sample numbers (N), standard length range, total weight range, and the length-weight relationship constants (a and b) for each species. In this study, we estimated the length-weight relationship of 16 freshwater fish species from some rivers of Morang district, Eastern Nepal. A total of 1,600 fish specimens, representing 16 different species from 5 families were studied from September 2022 to February 2023. The fishes were captured from the river and preserved in 20% formalin for subsequent biometric measurements in the laboratory. Biometric measurements were taken as follows: for each fish, length measurements were listed as standard length or fork length (SL in cm) from mouth to where the caudal fin is lobate. Length measurements were taken with a regular ruler validated against a Vernier Calliper, with an accuracy of 0.1 cm. Weight measurements were obtained using an electronic digital balance with a precision of 0.01 g. While listing weight, a fish consistency was maintained concerning the degree of wetness of the body to ensure accuracy. Among the species listed in the Morang district, Puntius terio has the smallest range of standard length (2.7 cm - 7.4 cm) and total weight (1.07 g - 7.06 g) while Garra gotyla gotyla has the largest range of standard length (4.3 cm - 18.6 cm) and total weight (4.5 g - 15.6 g). These variations indicate the natural size differences among the species. The analysis of the length-weight relationships revealed that all the studied fish species exhibited a negative allometric growth pattern. This means that as the length of the fish increases, its weight increases at a slower rate. The findings of this study contribute to our understanding of the growth patterns of freshwater fish species in the study area.

Encryption Gradient of Patients’ EMR using Forms of DICOM

Data protection is important. it is especially required for competent patient protection. If it is not done well, it can pose various problems. The problems of leakage can make patients vulnerable. This literally means that the healthcare environment can be threatened in this aspect. DICOM is a digitalized image compression technique using radiologic materials. It restores CT, PET-CT, and X-ray images in order to gain a specific image. It is then compiled to be sent as PACS. These imaging techniques use matrix as a data presenting method. However, it is sent in a linear form. It does not mean that it is not protected, but it means that there are various risks to be managed. In our report, we review that, in the future, a double layer of encryption with patient voice can dramatically evolve the probability of accessing patient healthcare data. This can also be applied in EMR or EHR in the future. The limitations of this study are that there are still risks of cyber-attack. The DDoS can totally make the system function down. However, we see this as a different problem as this is an electronic source matter rather than a hack of preserved data.

SOIL EROSION AND IMPACT ON RECREATIONAL RESOURCES IN THE SHYNGYRLAU BASIN, WESTERN KAZAKHSTAN: A MULTI-ANALYTICAL ASSESSMENT

Over the past decades, water erosion has increased significantly in the Shyngyrlau River basin. Recreational development, haphazard construction and operation of roads have led to increased water erosion and the formation of numerous linear erosion forms. Erosion reduces the natural resource status of the region. Water erosion develops in most cases along roads laid along the thalwegs of the ravine-hollow network. The light substrate along with sparse vegetation cover (the sparseness is aggravated by intensive grazing) predetermine its rapid development. Water erosion is an acute problem arising from the present climate change, agricultural intensification and diverse forms of anthropogenic land degradation. Assessment of present and potential soil erosion is useful for landscape preservation as well as development planning. Multi-analytical modeling can provide a quantitative and consistent estimation of soil erosion and sediment yield under locally specific environmental conditions. The soil loss model, Revised Universal Soil Loss Equation (RUSLE), integrated with GIS, has been used to estimate soil loss in the Shyngyrlau Basin (a left-bank tributary of the Ural River, NW Kazakhstan). The RUSLE model is based on remote sensing and field data; erosion probabilities were determined using GIS. The percentage ratio of the soil loss in the Shyngyrlau River basin shows erosion variation of 0.001–2.47 t/ha/yr. The degree of erosion increases with the length of the slope. A new factor Chip curvature (Cu factor), defining the accuracy of the soil loss results, was defined. According to this factor, soil erosion in the study area is 0.007–2.48 t/ha/yr within the low erosion class. The lowest indicator of the K factor is 0.2 in sandy clay soils used as pasturelands. The highest K factor (0.3) relates to clayey arable soils. The research results add to implementation of new strategies in soil management and conservation practices reducing soil erosion in the Shyngyrlau Basin. Both climate and anthropogenic factors are seen behind the activated ground erosion. The development of forms of water erosion leads to a violation of the integrity of modern natural complexes of the West Kazakhstan region, which significantly reduces their stability and recreational potential.

Results of a Study on the Impact of Surface Ozone Concentration on the Spread of COVID-19 in Tbilisi

The results of a study of the influence of diurnal values of surface ozone concentration (SOC) on the infection positivity rate with coronavirus COVID-19 (IR) of the population of Tbilisi from October 8, 2020 to May 31, 2021 are presented. It was found that IR values are inversely correlated with SOC. For example, at ozone concentrations from 0 to 20 mcg/m3 values of COVID-19 Infection Rate on average was 18.5 %, whereas with SOC values from 80 to 100 mcg/m3 – only 2.3%. Connection daily values of IR with SOC has an inverse linear form. IR = -0.2307·SOC + 20.543 for individual cases; IR = -0.2113·SOC + 19.756 for averaged values of IR in different ranges of SOC values.

In the search for all zeros of smooth functions

We consider the multi-valued problem of nding all solutions of the equation f(x) = 0 in the space of functions f : [0, 1] → R such that the derivative f(r) with r ∈ {0, 1, 2, . . .} exists and is Hölder continuous with exponent ϱ ∈ (0, 1]. Available algorithms use information about values of f and/or its derivatives at adaptively selected n points, and the error between the true solution Z(f) and approximate solution Zn(f) is measured by the Hausdor distance dH(Z(f),Zn(f)). We show that, despite the fact that the worst case error of any algorithm is innite, it is possible to construct nonadaptive approximations Z∗n such that the error dH (Z(f),Z∗n(f)) converges to zero as n → +∞. However, the convergence can be arbitrarily slow. Specically, for arbitrary sequence of approximations {Zn}n≥1 that use n adaptively chosen function values and/or its derivatives, and for arbitrary positive sequence {τn}n≥1 converging to zero there are functions f in our space such that supn≥1 τ−1n dH(Z(f),Zn(f))= +∞. We conjecture that the same lower bound holds if we allow information about values of n arbitrary and adaptively selected linear functionals at f.