Expansion Of Function Research Articles

The Memory Function of an Impurity in Mass and Hooke Constant in a Diatomic Chain

The memory function of an impurity with different mass and Hooke constant in a classical diatomic chain is studied by means of the recurrence relations method. The Laplace transform of the memory function has two pairs of resonant poles and three branch cuts. The poles contribute a cosine and the cuts contribute acoustic and optic branches, which are expressed as a convolution of a difference of two sines and an expansion of even-order Bessel functions. The expansion coefficients are integrals of Jacobian elliptic function sn(u) along the real axis in a complex u+iv plane for the acoustic branch, and integrals of nd(v) along a contour parallel to the imaginary axis of the plane for the optical branch, respectively. Different special cases are discussed in detail. It shows that a perfect monatomic or diatomic chain and such a chain with a mass impurity share the same memory function except for a constant factor, and that the pole contribution exists only if the impurity has both different mass and Hooke constant.

The Intervention of Digital Media Technology on the Visual Language of Radio and Television

Abstract This paper first explores the changes brought about by the convergence of digital media technology and radio and television. The SIFT feature extraction method is proposed based on the image signal characteristics, and the convolution operation is done on both the extracted image and the Gaussian kernel. In order to ensure the accurate localization of the key points of the image, the method of quadratic Taylor expansion of the DoG function is utilized to remove the unstable points, thus obtaining the accurate localization of the key points. Next, a 128-dimensional SIFT feature vector is generated by specifying the direction reference of the key point, and a visual dictionary is constructed on the basis of the generated feature vector. The impact of digital media technology on language intervention in radio and television is investigated through quantitative analysis and case studies. The results show that the scores of the image features after SIFT processing are in the interval of [13.342, 15.636], which is the highest score among the three methods, and the effect is better. The global digital media news parameter works increased by 240 works from 2013-2014 and reached the peak state of 732 works in 2021, and the public’s recognition of the visual language visualization of digital media news increased.

Modern Global Trends in the Development of Choral Performance

"The relevance of the studied issue is the need to identify the main trends in choral performance, and determine the principles of the work of conductors and choral artists in the context of renewal of the components in this field. The aim of the research is to study the problem of current global trends in the development of choral performance as a complex multifaceted and integral phenomenon. Its practical methods (audio search; audio selection; audio analysis) were used in the research. The aspects of modern choral performance (interdisciplinary; socio-cultural; as well as artistic management; professional training; modern engineering technologies; information and communication space; technologies aimed at preserving human and professional resources) were identified. The current components of activity in the field of modern choral art were established. The directions of modern choral practice were identified (activation of the musical group in the life of society; expansion of traditional executive functions; growth of the genre stylistic palette of the choral repertoire). The system of key modernized methods of interpreting choral works of the 20th and 21st centuries was studied (principles of intonation; the principle of expanding the range; the principle of enriching the technical means of interpretation; the principles of forming the performance texture; the principle of interpreting the verbal text in the context of the choral score; the principle of creating different types of sound). The general features of modern choral performance in Ukraine and in the world were studied. The results can be applied in the process of researching future choral performing practice and preparing the relevant studies. The prospects of research in this field of musical culture are to enrich the theoretical and practical sectors of choral art as a complex system which is open for updates. Keywords: choral art, choir, choral work, performance interpretation, choral genre, choral style, timbre dramaturgy, performance analysis."

Do Successful Researchers Reach the Self-Organized Critical Point?

The index of success of the researchers is now mostly measured using the Hirsch index (h). Our recent precise demonstration, that statistically h∼Nc∼Np, where Np and Nc denote, respectively, the total number of publications and total citations for the researcher, suggests that average number of citations per paper (Nc/Np), and hence h, are statistical numbers (Dunbar numbers) depending on the community or network to which the researcher belongs. We show here, extending our earlier observations, that the indications of success are not reflected by the total citations Nc, rather by the inequalities among citations from publications to publications. Specifically, we show that for highly successful authors, the yearly variations in the Gini index (g, giving the average inequality of citations for the publications) and the Kolkata index (k, giving the fraction of total citations received by the top (1−k) fraction of publications; k=0.80 corresponds to Pareto’s 80/20 law) approach each other to g=k≃0.82, signaling a precursor for the arrival of (or departure from) the self-organized critical (SOC) state of his/her publication statistics. Analyzing the citation statistics (from Google Scholar) of thirty successful scientists throughout their recorded publication history, we find that the g and k for the highly successful among them (mostly Nobel laureates, highest rank Stanford cite-scorers, and a few others) reach and hover just above (and then) below that g=k≃0.82 mark, while for others they remain below that mark. We also find that all the lower (than the SOC mark 0.82) values of k and g fit a linear relationship, k=1/2+cg, with c=0.39, as suggested by an approximate Landau-type expansion of the Lorenz function, and this also indicates k=g≃0.82 for the (extrapolated) SOC precursor mark.

Rational approximations of the Arrhenius and general temperature integrals, expansion of the incomplete gamma function

When analyzing materials non-isothermally using the Arrhenius equation under linear heating, a temperature integration is necessary. While the frequency factor in this equation is typically assumed to be constant, it can actually vary with temperature for certain solid-state reactions. The resulting temperature integral, known as the Arrhenius or general temperature integrals, usually have no analytical solutions. Therefore, special functions and approximation functions are often used to estimate them. In this particular study, new rational approximations for the Arrhenius and general temperature integrals were derived through the expansion of the incomplete gamma function. Two sets of these rational approximations, which exhibit excellent accuracy, are presented. One set of approximations for the Arrhenius integral matches the widely used Senum and Yang’s approximations, while the other set, which offers even greater accuracy, has not been previously reported. An obtained rational approximation has been utilized to simulate the thermal degradation of a commercially available PMMA, illustrating a practical application example.

Simple pendulum: period dependent on amplitude of oscillation

In this study, with a pedagogical aim suited for the undergraduate, the differential equations of motion that characterize and determine the motion of a simple pendulum were obtained considering small and large amplitudes of oscillation. These differential equations were solved through differential equation solution methods, numerical, expansion of functions and integrations. The solutions obtained using the different methods were compared. It was possible to verify, both experimentally and theoretically, that for the oscillatory movement of the simple pendulum, its oscillation period increases and its angular frequency decreases with the increase of the oscillation amplitude. The validity range of the approximation for small ranges of motion was also determined. It was verified that the theoretical and experimental results present a good agreement for angles smaller than 55°. The experimental measurements were made with “a low-cost home-built” equipment.

High-order models for convection–diffusion-reaction transport in multiscale porous media

Developing highly accurate models for predicting the convection–diffusion-reaction (CDR) transport in hierarchical porous media with strong heterogeneities on multiple scales is crucial but not yet available. In this work, an innovative high-order multiscale computational framework is developed to capture the local and global variation characteristics of flow fields and reactant concentration at multiple scales. The homogenized solutions and macro-meso high-order solutions are established by the formal two-scale asymptotic analysis. By directly expanding the mesoscopic cell functions to the microscopic levels, the three-scale high-order models are built by assembling the meso-micro high-order expansions of mesoscopic cell functions and macro-meso low/high-order models. The present approaches follow the reverse thought process of the reiteration homogenization method, and provide a very innovative way to develop highly accurate and efficient solutions for the CDR coupling problems in multiscale porous media. The effectiveness and accuracy of the proposed multiscale models are validated by several representative cases.

Maximum abdominal excursion assessment using an abdominal excursion measuring device: Reliability and validity of a new device for simple and quantitative assessment of respiratory function

This study aimed to verify the reliability and validity of abdominal expansion and respiratory function measurements. Forty healthy adult males underwent lung capacity, effort lung capacity, respiratory muscle strength, cough strength, diaphragm ultrasound, and abdominal expansion measurements. Abdominal expansion was measured using a device developed to accurately evaluate abdominal movements and calculate maximum abdominal expansion on the ventral side (AE-max: the difference between maximal abdominal contraction at the same time as maximal-effort expiration and maximal abdominal expansion at the same time as maximal-effort inspiration). Intra- and inter-rater reliabilities of the AE-max measurements were examined, the paired t-test was used for assessing the ratios of the expansion and contraction displacement components in AE-max, and regression analysis was used to obtain equations for predicting maximum inspiratory pressure (MIP) based on AE-max. Both intra- and inter-rater reliabilities were high. Criterion-related validity showed that AE-max was associated with all respiratory function parameters, especially MIP, and a high percentage of expansion displacement. Regression analysis showed that AE-max was significantly associated with MIP. Based on its association with MIP, the large proportion of expansion displacement in AE-max, and the results of the multiple regression analysis, we conclude that AE-max is a helpful measure for estimating MIP.

SOLUTION OF A MIXED BOUNDARY VALUE PROBLEM FOR THE LAPLACE EQUATION BY THE METHOD OF DIVIDING AN OBJECT IN A RECTANGULAR PARALLELEPIPED

The aim of the study is to solve the boundary value problem for the Laplace equation in a rectangular parallelepiped by the method of separation of variables and to estimate the obtained Fourier variable separation constants.
 
 Materials and methods. Methods of mathematical physics were used to solve the boundary value problem for the Laplace equation. The initial problem was divided into three standard ones, in which the inhomogeneous boundary conditions were given only on two parallel sides, for the rest of the problem they being assumed to be equal to 0.
 
 Results. The boundary value problem for the Laplace equation in a rectangular parallelepiped has been broken down into three problems. Partial solutions to these problems under given boundary conditions have been obtained. The Fourier variable separation constants are estimated.
 
 Findings. The solution to the Laplace’s equation for a parallelepiped is the sum of the solutions to three partial problems. The boundary functions of a parallelepiped are odd periodic over two variable functions whose periods are equal to the lengths of the corresponding sides of the parallelepiped. The Fourier constants of partial solutions to the problem are the coefficients of the expansion of the boundary periodic functions of two variables into a trigonometric Fourier series. In two-dimensional series of the solution to the Laplace’s equation for odd-numbered harmonics and for a set of simultaneously even and odd harmonics, the Fourier constants differ only in signs.

Role of Interface of Metal-Organic Frameworks and Their Composites in Persulfate-Based Advanced Oxidation Process for Water Purification.

The persulfate activation-based advanced oxidation process (PS-AOP) is an important technology in wastewater purification. Using metal-organic frameworks (MOFs) as heterogeneous catalysts in the PS-AOP showed good application potential. Considering the intrinsic advantages and disadvantages of MOF materials, combining MOFs with other functional materials has also shown excellent PS activation performance and even achieves certain functional expansion. This Review introduces the classification of MOFs and MOF-based composites and the latest progress of their application in PS-AOP systems. The relevant activation/degradation mechanisms are summarized and discussed. Moreover, the importance of catalyst-related interfacial interaction for developing and optimizing advanced oxidation systems is emphasized. Then, the interference behavior of environmental parameters on the interfacial reaction is analyzed. Specifically, the initial solution pH and coexisting inorganic anions may hinder the interfacial reaction process via the consumption of reactive oxygen species, affecting the activation/degradation process. This Review aims to explore and summarize the interfacial mechanism of MOF-based catalysts in the activation of PS. Hopefully, it will inspire researchers to develop new AOP strategies with more application prospects.

Efficacy of posture correction band vs. McKenzie's exercises on pulmonary function and chest expansion in asymptomatic population with forward head posture

BackgroundPoor posture and sedentary lifestyle cause Forward Head Posture (FHP). To correct this, a Posture Correction Band (PCB) is commonly used. However, the efficacy of PCB vs. McKenzie's Exercises on pulmonary function and chest expansion in asymptomatic individuals with FHP was not known. Objective: This study aimed to determine the efficacy of PCB vs. McKenzie's Exercises on the Pulmonary function and chest expansion in asymptomatic population with FHP. Methodology: A Randomized control trial was conducted on forty-two subjects with FHP. Subjects were divided in two groups. G1 group was educated as per McKenzie's exercises to perform once daily for a month. The Pulmonary function test and chest expansion of this group was performed before and after the McKenzie exercises. G2 group wore PCB for 2 h daily for a month and their PFT and chest expansion was recorded before and after the trial. FVC, FEV1, FEV1/FVC ratio, PEFR and Chest expansion were measured. Results: The P-value of FVC, FEV1, FEV1/FVC ratio and PEFR between the groups (treatment group) was significant as 0.000, 0.000, 0.000 and 0.02 respectively. The chest expansion was non-significant between the groups (treatment group) with P-value as 0.553, 0.493 and 0.699 at axillary, 4th intercostal and xiphisternum level respectively. The P-value of FVC, FEV1, FEV1/FVC ratio and PEFR between the groups (control group) was non-significant as 0.682, 0.149, 0.424 and 0.414 respectively. The chest expansion was also non-significant between the groups (control group) with P-value as 0.853, 0.651 and 0.763 at axillary, 4th intercostal and xiphisternum level. Conclusion: The study concluded that there were significant effects of both Posture Correction Band and Mc’Kenzie exercises on pulmonary function with greater difference seen with PCB and non-significant effects on chest expansion in terms of P-values in treatment group.

Structure-Function Analysis of p57KIP2 in the Human Pancreatic Beta Cell Reveals a Bipartite Nuclear Localization Signal.

Mutations in CDKN1C, encoding p57KIP2, a canonical cell cycle inhibitor, underlie multiple pediatric endocrine syndromes. Despite this central role in disease, little is known about the structure and function of p57KIP2 in the human pancreatic beta cell. Since p57KIP2 is predominantly nuclear in human beta cells, we hypothesized that disease-causing mutations in its nuclear localization sequence (NLS) may correlate with abnormal phenotypes. We prepared RIP1 insulin promoter-driven adenoviruses encoding deletions of multiple disease-associated but unexplored regions of p57KIP2 and performed a comprehensive structure-function analysis of CDKN1C/p57KIP2. Real-time polymerase chain reaction and immunoblot analyses confirmed p57KIP2 overexpression, construct size, and beta cell specificity. By immunocytochemistry, wild-type (WT) p57KIP2 displayed nuclear localization. In contrast, deletion of a putative NLS at amino acids 278-281 failed to access the nucleus. Unexpectedly, we identified a second downstream NLS at amino acids 312-316. Further analysis showed that each individual NLS is required for nuclear localization, but neither alone is sufficient. In summary, p57KIP2 contains a classical bipartite NLS characterized by 2 clusters of positively charged amino acids separated by a proline-rich linker region. Variants in the sequences encoding these 2 NLS sequences account for functional p57KIP2 loss and beta cell expansion seen in human disease.

Low-frequency Internal Gravity Waves Are Pseudo-incompressible

Starting from the fully compressible fluid equations in a plane-parallel atmosphere, we demonstrate that linear internal gravity waves are naturally pseudo-incompressible in the limit that the wave frequency ω is much less than that of surface gravity waves, i.e., ω≪gkh , where g is the gravitational acceleration and k h is the horizontal wavenumber. We accomplish this by performing a formal expansion of the wave functions and the local dispersion relation in terms of a dimensionless frequency ε=ω/gkh . Further, we show that, in this same low-frequency limit, several forms of the anelastic approximation, including the Lantz–Braginsky–Roberts formulation, poorly reproduce the correct behavior of internal gravity waves. The pseudo-incompressible approximation is achieved by assuming that Eulerian fluctuations of the pressure are small in the continuity equation—whereas, in the anelastic approximation, Eulerian density fluctuations are ignored. In an adiabatic stratification, such as occurs in a convection zone, the two approximations become identical. However, in a stable stratification, the differences between the two approximations are stark and only the pseudo-incompressible approximation remains valid.

EHBP1 Is Critically Involved in the Dendritic Arbor Formation and Is Coupled to Factors Promoting Actin Filament Formation.

The coordinated action of a plethora of factors is required for the organization and dynamics of membranous structures critically underlying the development and function of cells, organs, and organisms. The evolutionary acquisition of additional amino acid motifs allows for expansion and/or specification of protein functions. We identify a thus far unrecognized motif specific for chordata EHBP1 proteins and demonstrate that this motif is critically required for interaction with syndapin I, an F-BAR domain-containing, membrane-shaping protein predominantly expressed in neurons. Gain-of-function and loss-of-function studies in rat primary hippocampal neurons (of mixed sexes) unraveled that EHBP1 has an important role in neuromorphogenesis. Surprisingly, our analyses uncovered that this newly identified function of EHBP1 did not require the domain responsible for Rab GTPase binding but was strictly dependent on EHBP1's syndapin I binding interface and on the presence of syndapin I in the developing neurons. These findings were underscored by temporally and spatially remarkable overlapping dynamics of EHBP1 and syndapin I at nascent dendritic branch sites. In addition, rescue experiments demonstrated the necessity of two additional EHBP1 domains for dendritic arborization, the C2 and CH domains. Importantly, the additionally uncovered critical involvement of the actin nucleator Cobl in EHBP1 functions suggested that not only static association with F-actin via EHBP1's CH domain is important for dendritic arbor formation but also actin nucleation. Syndapin interactions organize ternary protein complexes composed of EHBP1, syndapin I, and Cobl, and our functional data show that only together these factors give rise to proper cell shape during neuronal development.

DNA Secret Writing With Laplace Transform of Mittag-Leffler Function

In this study, we present a new cryptosystem named Deoxyribose Nucleic Acid (DNA) secret writing with the Laplace transform of the Mittag-Leffler function. The method is proper for encrypting large files. In this technique, we consider the original message as binary sequence. These binary streams corresponding to the plain text is transformed to DNA bases by utilizing DNA encoding, then the DNA codes are transformed to positive integers. We apply the Laplace transform to these numbers which are coefficients of the expansion of the Mittag-Leffler function. To provide multi-stage protection, the outcome coefficients are transformed to binary sequences and other level of encryption with cumulative XOR is applied and equivalent MSBs obtained at every iteration are utilized for building cipher text. Decryption is implemented in the opposite way. We employ monobit test, correlation analysis for measuring the reliability of encryption, and Python programming language to obtain secret message, the plain text, and computations of statistical tests.

Orientation Quaternion Norm Correction in SINS Algorithms: Calculation Normalization Schemes and Their Efficiency

The problem of correcting the norm of the computed orientation quaternion in the algorithms for the operation of strapdown inertial navigation systems is considered. Two existing approaches to the correction process are considered, the first approach is to normalize the rotation quaternion at the computation cycle, the second approach is to normalize the resulting quaternion. 5 well-known calculation schemes for norm correction are given. To simulate the test motion, we used an analytical quaternion kinematic rotation model based on a sequence of three rotations corresponding to the Krylov angles. The case of linear dependence of elementary rotation angles on time is considered. The model provides analytical representation of the projections of the angular velocity vector of the rigid body on the associated axes and the corresponding quasi-coordinates on the calculation cycle. The results of numerical simulation of the reference motion for a given set of frequencies are presented as dependences of the projections of the angular velocity vector of the rigid body on time and the constructed trajectories in the configuration space of the orientation parameters.
 To determine the rotation quaternion on a cycle, the Miller algorithm was used, which makes it possible to obtain an increase in the orientation vector based on ideal information from the angular velocity sensors in the form of quasi-coordinates. The transformation into a rotation quaternion occurs with the help of the corresponding expansions of the trigonometric functions of the true rotation angle (modulus of the orientation vector) in a series.
 Based on a numerical experiment, it is shown that the best result of correcting the norm of the calculated quaternion in the sense of the minimum error of the norm is given by one of the finite normalization schemes, for which there is no division operation and ensures the stability of the norm correction in time. The results of numerical simulation of the model rotational motion of a rigid body and the development of schemes for correcting the norm of the calculated orientation quaternion are presented.
 Keywords: orientation quaternion, Miller's orientation algorithm, SINS, norm error, computational drift, analytical reference model, quasi-coordinates, numerical simulation.

MultiHypExp: A Mathematica package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms

We present the Mathematica package MultiHypExp that allows for the expansion of multivariate hypergeometric functions (MHFs), especially those likely to appear as solutions of multi-loop, multi-scale Feynman integrals, in the dimensional regularization parameter. The series expansion of MHFs can be carried out around integer values of parameters to express the series coefficients in terms of multiple polylogarithms. The package uses a modified version of the algorithm prescribed in [1]. In the present work, we relate a given MHF to a Taylor series expandable MHF by a differential operator. The Taylor expansion of the latter MHF is found by first finding the associated partial differential equations (PDEs) from its series representation. We then bring the PDEs to the Pfaffian system and further to the canonical form, and solve them order by order in the expansion parameter using appropriate boundary conditions. The Taylor expansion so obtained and the differential operators are used to find the series expansion of the given MHF. We provide examples to demonstrate the algorithm and to describe the usage of the package, which can be found in this url. Program summaryProgram Title:MultiHypExp.wl version 1.0CPC Library link to program files:https://doi.org/10.17632/zxwkx38y7b.1Developer's repository link:https://github.com/souvik5151/MultiHypExpLicensing provisions: GNU General Public License 3Programming language: Wolfram Mathematica version 11.3 or higherExternal routines/libraries: HolonomicFunctions, CANONICA, HYPERDIRE, PolyLogTools, HPLNature of problem: Obtaining the series expansion of multivariate hypergeometric functions around integer values of Pochhammer parameters in terms of multiple polylogarithmsSolution method: Mathematica implementation of a modified version of the algorithm prescribed in Nucl. Phys. B 989 (2023) 116145.

Truncated Cauchy Power Kumaraswamy Generalized family of distributions: Theory and Applications

A new family called the Truncated Cauchy Power Kumaraswamy -G family of distributions is proposed. Some special models of this family are introduced. Statistical properties of the family such as expansion of density function, moments, incomplete moments, mean deviation, bonferroni and Lorenz curves are proposed. We discuss the method of maximum likelihood to estimate the model parameters and study its performance by simulation. Real data sets are modeled to illustrate the importance and exibility of the proposed model in comparison to some known ones yielded favourable results.

Impact of asymmetric electrodes on ferroelectricity of sub-10 nm HZO thin films

In this study, platinum (Pt) and tungsten (W), two materials with dissimilar coefficients of thermal expansion (CTE) and work functions (WF), are used as the top electrode (TE) and the bottom electrode (BE) in metal/ferroelectric/metal (MFM) structures to explore the ferroelectricity of hafnium zirconium oxide (HZO) with a thickness less than 10 nm. The electrical measurements indicate that a higher CTE mismatch between HZO and TE/BE is beneficial for enhancing the ferroelectric properties of nanoscale HZO thin films. The different WFs of TE and BE generate a built-in electric field in the HZO layer, leading to shifts in the hysteresis loops and the capacitance–voltage characteristics. The structural characterizations reveal that the preferred formation of the orthorhombic phase in HZO is dominated by the W BE. The device in which W is used as the TE and BE (the W/HZO/W MFM structure) presents the optimal ferroelectric performance of a high remanent polarization (2P r = 55.2 μC cm−2). The presence of tungsten oxide (WO x ) at the W/HZO interfaces, as revealed by high-resolution transmission microscopy, is also responsible for the enhancement of ferroelectric properties. This study demonstrates the significant effects of different CTEs and WFs of TE and BE on the properties of ferroelectric HZO thin films.

An Improved Model of Wavelet Leader Covariance for Estimating Multifractal Properties

Complex systems often produce multifractal signals defined by stationary increments that exhibit power-law scaling properties. The Legendre transform of the domain-dependent scaling function that defines the power law is known as the multifractal spectrum. The multifractal spectrum can also be defined by a power-series expansion of the scaling function and in practice the first two leading coefficients of that series are estimated from the discrete wavelet transform of the signal. To quantify, validate, and compare simulations of complex systems with data collected empirically from the actual system, practitioners require methods for approximating the variance associated with estimates of these coefficients. In this work, we generalize a previously developed semi-parametric statistical model for the values extracted from a discrete multi-scale wavelet transform to include both within-scale and between-scale covariance dependencies. We employ multiplicative cascades to simulate multifractals with known parameters to illustrate the necessity for this generalization and to test the precision of our improved model. The combined within- and between-scale model of covariance results in a more accurate estimate of the expected variance of the coefficients extracted from an empirical data set.