Related Formulas Research Articles

Deciphering Guarapachangueo: Formulas and Formulaic Variation in Contemporary Rumba Percussion

This article serves to further the conceptual and musical analysis of guarapachangueo, a key influence in the contemporary style of the percussion in Havana-style rumba. I follow Turino’s (2009) lead in distinguishing between improvisation and formulaic performance in analyzing the rhythmic vocabulary of guarapachangueo as a set of related formulas and variations. In doing so, I expand upon and refine some of the characteristics of guarapachangeuo described by Bodenheimer (2015), particularly the common and yet nebulous idea that the style entails increased improvisation in the lower register of the percussion. As an active performer of the style who specializes in the lower register percussion, I will draw upon my experiences and those of fellow rumberos, as well as commercial recordings and online videos of rumba in highlighting the structural formulas used in rumba’s contemporary rhythmic vocabulary. I argue that rather than increased improvisation, guarapachangueo comprises an aesthetic approach to playing rumba in which unique formulas are employed, representing a break with the standardized formulas of traditional rumba from the second half of the 20th century. These formulas produce a heightened sense of tension and release in which increased space and the interactive exchange of percussive phrases are central. Internalized by drummers, these formulas and variations become part of the performer’s musical habitus and are drawn upon—often unconsciously—by the musicians in the form of musical decisions that “say something” in the flow of a rumba performance.

Reliability Analysis of Cold-standby Systems with Subsystems Using Conditional Binary Decision Diagrams

<p>Cold-standby systems have been widely used for conditions with limited power, which achieve fault tolerance and high-reliability systems. The cold spare (CSP) gate is a common dynamic gate in the dynamic fault tree (DFT). DFT with CSP gates is typically used to model a cold-standby system for reliability analysis. In general, inputs of the CSP gate are considered to be basic events. However, with the requirement of the current system design, the inputs of the CSP gate may be either basic events or top events of subtrees. Hence, the sequence-dependency among basic events in CSP gates becomes much more complex. However, the early conditional binary decision diagram (CBDD) used for the reliability analysis of spare gates does not consider it well. To address this problem, the conditioning event rep is improved to describe the replacement behavior in CSP gates with subtrees inputs, and the related formulae are derived. Further, a combinatorial method based on the CBDD is demonstrated to evaluate the reliability of cold-standby systems modeled by CSP gates with subtrees inputs. The case study is presented to show the advantage of using our method.</p> <p> </p>

Evaluation of functional relation formula for the Clausen and Glaisher functions and multiple L-values

Evaluation of functional relation formula for the Clausen and Glaisher functions and multiple L-values

Mechanical properties of short polypropylene fiber enhanced recycled concrete under cyclic compression

AbstractThis study investigated the mechanical properties and stress–strain relationship of polypropylene fiber recycled aggregate concrete (PFRAC) subjected to uniaxial cyclic compression. A total of 78 cylindrical specimens were designed for uniaxial cyclic compression test with coarse aggregate replacement rate, polypropylene fiber volume fraction, and loading rate as variation parameters. The failure process of the specimens under cyclic loading was observed and recorded. The stress–strain curve of PFRAC was summarized. The important mechanical properties of PFRAC were obtained, such as plastic strain, accumulated energy dissipation. The microstructure of PFRAC was analyzed by scanning electron microscopy, and the crack resistance mechanism of PFRAC under cyclic loading was revealed. The results show that the PFRAC under cyclic loading appeared oblique splitting failure. The compressive stress–strain curve envelope of PFRAC subjected to cyclic loading exhibited similarity to the monotonic counterpart. The addition of polypropylene fibers can improve the peak stress, peak strain, residual stress, post‐peak ductility, and accumulated energy dissipation of the recycled concrete. In addition, a constitutive relation formula for the PFRAC stress–strain curve under cyclic loading is proposed, and the fitting result is good.

Connexive Logic, Probabilistic Default Reasoning, and Compound Conditionals

We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the form if not-A, thenA, should not hold, since the conditional’s antecedent not-A contradicts its consequent A. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event A|A¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${A| \\overline{A}}$$\\end{document} is p(A|A¯)=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${p(A| \\overline{A})=0}$$\\end{document}. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles: Aristotle’s theses, Aristotle’s Second Thesis, Abelard’s First Principle, and Boethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (like non-symmetry). Both approaches satisfy minimal requirements for a connexive logic. Finally, we compare both approaches conceptually.

Twisted Linear Periods and a New Relative Trace Formula

Twisted Linear Periods and a New Relative Trace Formula

(Invited) high speed densely dispersion-managed soliton and four-wave-mixing in dense periodical fibers and conventional dispersion-managed systems

I briefly reviewed the interesting densely dispersion-managed soliton (DDMS), and single channel high speed (40–160 Gbit/s) DDMS can transmit record distance at that time. I briefly reviewed the four-wave-mixing (FWM) of continous wave (CW) lasers in DPF when the EDFAs are located in the middle of dispersion section (z2 section), and our relative FWM efficiency formula was the first formula even for conventional dispersion-managed system (CDM) as well. We reached much lower FWM efficiency over a broad wavelength range in the well designed DPF than that in CDM and constant dispersion systems. We first found the FWM resonant condition for our dense periodical fiber (DPF) and CDM system. FWM strongly relates to the location of EDFAs. In this paper, I first report the analytical formula of relative FWM of CW lasers in DPF when the EDFAs are located right after the z1 section with dispersion D1, and our results are also suitable for CDM systems.

Trigonometric Sums and Riemann Zeta Function

ABSTRACTSeveral trigonometric sums are examined by means of partial fraction decompositions. Their generating functions will be evaluated in closed forms and the related asymptotic formulae in terms of Riemann zeta function will be established.

Manin–Drinfeld cycles and derivatives of $L$-functions

We study algebraic cycles in the moduli space of \operatorname{PGL}_2 -shtukas, arising from the diagonal torus. Our main result shows that their intersection pairing with the Heegner–Drinfeld cycle is the product of the r -th central derivative of an automorphic L -function L(\pi,s) and Waldspurger's toric period integral. When L(\pi,1/2) \neq 0 , this gives a new geometric interpretation for the Taylor series expansion. When L(\pi,1/2) = 0 , the pairing vanishes, suggesting higher order analogues of the vanishing of cusps in the modular Jacobian, as well as other new phenomena. Our proof sheds new light on the algebraic correspondence introduced by Yun and Zhang, which is the geometric incarnation of “differentiating the L -function”. We realize it as the Lie algebra action of e+f \in \mathfrak{sl}_2 on (\mathbb{Q}_\ell^2)^{\otimes 2d} . The comparison of relative trace formulas needed to prove our formula is then a consequence of Schur–Weyl duality.

Experimental investigation on mechanical properties of steel fiber reinforced recycled aggregate concrete under uniaxial cyclic compression

The performance of steel fiber reinforced recycled concrete (SF-R-RAC) under cyclic loading plays an important role in studying the response of recycled concrete structures under earthquake. In this paper, the effects of three design variables— the replacement rate of recycled aggregate, the content of steel fiber (SF), and the loading rate— on the stress–strain relationship and mechanical properties of SF-R-RAC specimens under cyclic loading were investigated. The failure mode of SF-R-RAC under cyclic action was observed, and the law of the cyclic stress–strain curve was summarized. In addition, the influence of different design variables on stiffness degradation and hysteretic energy dissipation of specimens under cyclic loading was described, which reveals the plastic strain law of SF-R-RAC under cyclic action. Finally, a piecewise function was used to fit the envelope of the cyclic stress–strain curve. The results show that adding SF to the recycled concrete specimen improves its ductility under uniaxial cyclic loading, delays the stiffness degradation rate of the specimen, and greatly improves its cumulative energy consumption. In addition, a constitutive relation formula for the SF-R-RAC stress–strain curve expressed by SF content is proposed, and the fitting result is good. This investigation provides a theoretical basis and an experimental reference for further study of SF-R-RAC.

Quadratic phase S-Transform: Properties and uncertainty principles

In this paper, a novel quadratic phase S-transform (QPST) is proposed, by generalizing the S-transform (ST) with five parameters a, b, c,d and e. QPST displays the time and quadratic phase domain-frequency information jointly in the time-frequency plane. Firstly, we define the novel QPST and give its relation with quadratic phase Fourier transform (QPFT). Secondly, several important properties of newly defined QPST, such as conjugation, translation, modulation, orthogonality relation and reconstruction formula are derived. Finally, we formulate several classes of uncertainty inequalities, such as the Heisenberg uncertainty inequality and logarithmic uncertainty inequality.

An iteratively reweighted time-domain acoustic method for reconstructing the transient acoustic field

An improved iterative reweighted least-squares based on real-time near-field acoustic hologram method (RTNAH) is proposed to reconstruct the transient acoustic field. First, time-domain convolution relation formula between the pressure time-wavenumber spectra on the hologram and reconstruction planes is first established by an impulse response function, and the corresponding matrix equation is obtained. Then, for solving the pressure spectra on the reconstruction plane, an improved iterative reweighted least-squares algorithm is applied for solving the minimization problem of the sum of 2-norm residual and 2-norm weighted solution under the weighted and sparse representation framework. By controlling the iteratively updated weighting matrix, the sparsity of the solution is promoted. Finally, the pressure spectra of the reconstruction plane are estimated, and the corresponding time-varying pressures are acquired by the two-dimensional inverse Fourier transform. A numerical simulation is conducted to observe the reconstruction capacity of the proposed method. The simulation results demonstrate that the proposed method can reconstruct the transient acoustic field in time-space domains very well. Meanwhile, several vital parameters are discussed, and the superiorities of the proposed method are testified by comparing to RTNAH with Tikhonov regularization and YALL1 model. An experiment is implemented for further validating the effectivity of the proposed method.

Complexes of NiII, CoII, ZnII, and CuII with Promising Anti-Tuberculosis Drug: Solid-State Structures and DFT Calculations

Four new NiII, CoII, ZnII, and CuII complexes with the promising anti-tuberculosis drug (E/Z)-N′-((5-Hydroxy-3,4-bis(hydroxymethyl)-6-methylpyridin-2-yl)methylene)-isonicotino-hydrazide (LH) were synthesized and characterized by structural methods: single-crystal X-ray diffraction, vibrational spectroscopy, and mass spectrometry. The NiII, CoII, and ZnII metal ions form only amorphous phases with various morphologies according to mass spectrometry and IR spectroscopy. The CuII forms a crystalline 1D coordination polymer with the relative formula {[CuLCl]·0.5H2O}∞1. Even though the LH ligand in the crystalline state includes a mixture of E-/Z-isomers, only the tautomeric iminol E-/Z-form is coordinated by CuII in the crystal. The copper(II) complex crystallizes in the monoclinic P21/n space group with the corresponding cell parameters a = 16.3539(11) Å, b = 12.2647(6) Å, and c = 17.4916(10) Å; α = 90°, β = 108.431(7)°, and γ = 90°. DFT calculations showed that the Z-isomer of the LH ligand in solution has the lowest formation energy due to intramolecular hydrogen bonds. According to the quantum chemical calculations, the coordination environment of the CuII atom during the transfer of the molecule into the solution remains the same as in the crystal, except for the polymeric bond, namely, distorted trigonal bipyramidal. Some of the complexes investigated can be used as effective sensors in biosystems.

Magnetization dynamics in layered systems with coexisting bilinear and biquadratic interlayer exchange coupling

Important aspects of exchange-coupled magnetic layered structures are related to the noncollinear arrangement of sublayer magnetizations which can arise from competition between bilinear (BL) and biquadratic (BQ) interlayer exchange coupling (IEC). In this work, the influence of coexisting BL and BQ IEC of different strengths on magnetization precession in layered systems is investigated both experimentally and theoretically. Laser-induced magnetization precession has been studied in the $\text{Fe/Si}({d}_{\text{Si}}$) multilayers (MLS) as a function of the amplitude ($H$) and orientation angle (${\ensuremath{\theta}}_{H}$) of external magnetic field using time-resolved magneto-optical Kerr (TRMOKE) effect. Strongly changing characters of precession frequency dependencies $\ensuremath{\omega}(H,{\ensuremath{\theta}}_{H})$ for Fe sublayer thickness ${d}_{\text{Fe}}=3$ nm and Si spacer-layer thicknesses (${d}_{\text{Si}}$) varying in the range of 0.9--2.4 nm have been observed. Analytical formulas for acoustic and optic mode dispersion relations with coexisting BL and BQ IEC, scaled by ${J}_{1}$ and ${J}_{2}$ parameters, respectively, for the in-plane effective magnetic anisotropy and arbitrary magnetic field direction were derived, and very good agreement with the experimentally observed frequency dependencies has been obtained. It is shown that BQ coexisting with BL IEC significantly influences on the magnitude and form of dispersion relations. From analytical formula derived, it follows that zero-field optical mode frequency tends to zero as $|{J}_{1}|$ approaches $2{J}_{2}$. The acoustic and optic mode-crossing effect has been observed and it is found that values of crossing fields and frequency gaps strongly increase as ${\ensuremath{\theta}}_{H}$ angles decrease and depend on relative BL and BQ IEC strengths. The BL IEC is of ferromagnetic type with ${J}_{1}\ensuremath{\approx}1.6$ mJ/${\mathrm{m}}^{2}$ for the MLS with ${d}_{\text{Si}}=0.9$ nm, and changes to antiferromagnetic one with ${J}_{1}\ensuremath{\approx}\ensuremath{-}0.9$ mJ/${\mathrm{m}}^{2}$ for the MLS with ${d}_{\text{Si}}=1.4$ nm, while the ${J}_{2}$ parameter of BQ IEC decreases from 1.8 to 1.0 mJ/${\mathrm{m}}^{2}$. The coupling strengths decrease by one to two orders of magnitude for the sample with ${d}_{\text{Si}}=2.4$ nm, but both mode frequencies are still observed and well reproduced by the theory. It is shown that ${J}_{1}$ and ${J}_{2}$ parameters obtained in the TRMOKE experiment coincide within the estimated error bars with the determined from independent measurements of magnetization processes in the static magneto-optical Kerr effect and interpreted with the use of analytical formulas derived. Numerical solutions of coupled Landau-Lifshitz-Gilbert (LLG) equations for acoustic and optic modes, with inclusion of BL IEC, intrinsic Gilbert damping, and spin-pumping damping terms, and extended to include BQ IEC, were performed and fitted to experimental data. It is shown that determined effective damping coefficients on $H$ and ${\ensuremath{\theta}}_{H}$ dependencies for acoustic and optic modes are very well simulated with the use of LLG equation solutions with Gilbert damping, spin-pumping-damping--related effective spin-mixing conductance, and spin-diffusion length parameters included. The dependencies of the parameters on ${d}_{\text{Si}}$ spacer-layer thickness are discussed and compared with available data for other systems.

Hybrinomials related to hyper-Leonardo numbers

In this paper, we define hybrinomials related to hyper-Leonardo numbers. We study some of their properties such as the recurrence relation and summation formulas. In addition, we introduce hybrid hyper Leonardo numbers.

Biodiversity and Spatial Distribution of Mosquitoes (Diptera: Culicidae) in Kurdistan Province, Western Iran.

Mosquitoes (Diptera: Culicidae) have always been considered as the vector/s of viral and parasitic diseases. This study aimed to conduct a comprehensive survey on the species composition, spatial distribution, and biodiversity indices of mosquitoes in Kurdistan Province, western Iran. This study was carried out in 10 counties of Kurdistan Province. The immature stages of mosquitoes were collected monthly from June to September. ArcGIS software was used to spatial analysis and create maps. Alpha diversity indices were calculated using the related formula. Totally, 5831 larvae belonging to the family Culicidae were collected. Twelve species were identified including: Anopheles claviger, An. maculipennis s.l, An. superpictus s.l, Culiseta. longiareolata, Cs. subochrea, Culex hortensis, Cx. mimeticus, Cx. perexiguus, Cx. pipiens, Cx. theileri, Cx. modestus and Cx. territans. Based on this analysis, the high-risk areas of the province are determined as Anopheles in the west, Culex in the north, and the Culiseta in the south of the province. Analyzing the Alpha biodiversity indices showed Baneh and Sarabad had the maximum and Bijar had the minimum mosquito biodiversity. The western counties of the province are regarded as the hotspots for anopheline mosquitos. Moreover, reporting of malaria cases in the past, bordering with Iraq and the high traffic of travelers have made these areas as potential foci for malaria transmission. So that, routine entomological inspections are proposed to detect any suspicious vector or case entrance.

Increasing Growth of Renewable Energy: A State of Art

The growth of renewable energy actively takes part in decarbonizing the fossil-fuel-based energy system. It reduces carbon emissions, carbon footprint, and greenhouse gas emissions and increases clean energy. The usage of renewable resources reduces and solves several problems, such as increasing temperature, carbon footprint, greenhouse gas emissions, and energy waste. Every sector contributes to increasing the above-mentioned factors in the environment. One of the main reasons for this biodegradation and climate change is energy resources. Using renewable energy instead of fossil fuel can solve the problem. This paper aims to find open research problems about the application of renewable energy and to initiate new innovative ideas regarding renewable energy. A detailed state of the art includes trends for renewable energy resources, their theoretical evolution, and practical implementations. Methodologies used for decision analysis in renewable energy are discussed in detail. The time frame for this analysis of renewable energy is 2010 to >2022. An extensive literature review finds a huge research scope in applying renewable energy in other research, such as logistics, smart production management, and advanced inventory management. Then, major changes in the profit/cost of that system due to renewable energy can be analyzed. This research proposes some innovative new ideas related cost formulas for renewable energy for the corresponding open problems.

Composite Quantum Coriolis Forces

In a consistent quantum theory known as “non-Hermitian interaction picture” (NIP), the standard quantum Coriolis operator Σ(t) emerges whenever the observables of a unitary system are given in their quasi-Hermitian and non-stationary rather than “usual” representations. With Σ(t) needed, in NIP, in both the Schrödinger-like and Heisenberg-like dynamical evolution equations we show that another, amended and potentially simplified theory can be based on an auxiliary N−term factorization of the Dyson’s Hermitization map Ω(t). The knowledge of this factorization is shown to lead to a multiplet of alternative eligible Coriolis forces Σn(t) with n=0,1,…,N. The related formulae for the measurable predictions constitute a new formalism refered to as “factorization-based non-Hermitian interaction picture” (FNIP). The conventional NIP formalism (where N=1) becomes complemented by an (N−1)-plet of its innovative “hybrid” alternatives. Some of the respective ad hoc adaptations of observables may result in an optimal representation of quantum dynamics.

Efficient computation of oscillatory Bessel transforms with a singularity of Cauchy type

In this article, we present and analyze efficient methods for computing the Cauchy principal value integral of the oscillatory Bessel function ∫abf(x)x−cJm(ωx)dx, where 0≤a<c<b. For the two cases of a>0 and a=0, we establish new steepest descent integration paths, and employ the complex line integration technique to obtain affordable quadrature rules. According to the relation formula between the Meijer G-function and the Bessel function, a crucial explicit expression of the required integral ∫0+∞xjx−cJm(ωx)dx can be derived in terms of the Meijer G-function. Furthermore, for the proposed quadrature formulae, we perform rigorous error analysis in inverse powers of ω. Particularly, compared with a combination method given in the work (Kang et al., 2022), the proposed method takes less time and produces more accurate results. We verify error analysis of the proposed method by experimental results. Numerical examples are presented to illustrate the accuracy and efficiency of the proposed numerical methods.

Global Asset Allocation Based on Principal Component Risk Parity Model

Contemporarily, as the economy enters the new normal, Chinese real estate prices that rose almost unilaterally in the past will be difficult to appear again. With just break, the high yield of wealth management products will no longer be the scene. Therefore, the importance of risk diversification among different assets, i.e., the allocation decision of major assets, becomes more and more prominent. This paper mainly investigates the application of principal component risk parity model in asset allocation. Specifically, the article focuses on the result of the experiment and the importance of this model. In the experiment, the principal component risk parity model is compared with the traditional risk parity model. At the same time, the principal component parity risk model is further analyzed and compared with other models from the related formulae derivation. Finally, the corresponding conclusions are drawn, and the advantages and necessity of rational usage of risk parity model in asset allocation are put forward. Overall, these results shed light on guiding further exploration of finding efficient models to help with asset allocation.