Point Formula Research Articles

Symmetry classification and enumeration of square-tile sikku kolams

Pulli kolam is an ancient mathematical art form that is still practiced today in south India by over a quarter million people. ‘Pulli’ in the Tamizh language means ‘dots’. A specific type of pulli kolam is sikku kolam where a series of dots are placed using rice flour and lines are drawn around them following three simple rules. Here we focus on sikku kolams assembled from square tiles. Kolams are classified by their point group symmetry and formulae are derived for counting the number of kolams of each symmetry type. Some interesting constraint problems are posed that could help formulate new games based on this elegant art form.

Superconformal indices and localization in N = 2B quantum mechanics

Superconformal ‘type B’ quantum mechanical sigma models arise in a variety of interesting contexts, such as the description of D-brane bound states in an AdS2 decoupling limit. Focusing on N = 2B models, we study superconformal indices which count short multiplets and provide an alternative to the standard Witten index, as the latter suffers from infrared issues. We show that the basic index receives contributions from lowest Landau level states in an effective magnetic field and that, due to the noncompactness of the target space, it is typically divergent. Fortunately, the models of interest possess an additional target space isometry which allows for the definition of a well-behaved refined index. We compute this index using localization of the functional integral and find that the result agrees with a naive application of the Atiyah-Bott fixed point formula outside of it’s starting assumptions. In the simplest examples, this formula can also be directly verified by explicitly computing the short multiplet spectrum.

Degree of the 3-secant variety

In this paper, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 5-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of the double point formula to reduce the calculation into the case of the 2-secant variety. As a resolution of the 2-secant variety, we use secant bundle and compute powers of desired algebraic cycles.

ANALISIS BREAK EVEN POINT SEBAGAI ALAT PERENCANAAN LABA PADA UD BUMI TANI KABUPATEN LUWU UTARA

This research aims to analyze the break-even point as a profit planning tool for UD. Bumi Tani in North Luwu Regency. The research variable is profit planning, measured through break-even point analysis. The study population consists of data related to break-even point analysis, including costs, sales, gross profit, and net profit for UD. Bumi Tani in North Luwu Regency during the period 2020-2022. The sample used encompasses the entire population under study, including data on costs, sales, gross profit, and net profit for UD. Bumi Tani in North Luwu Regency during the period 2020-2022. Data collection was conducted using documentation techniques and interviews. Data analysis employed the break-even point formula, margin of safety, and profit planning calculations. The research findings reveal the break-even point in 2020 amounted to Rp19,422,070,314, increasing by 34.7% to Rp26,160,792,733 in 2021, and further rising by 17.5% to Rp30,751,220,045 in 2022. The margin of safety in 2020 was 40.5%, increasing to 42% in 2021, and further rising to 45.1% in 2022. The profit planning results indicate a projected sales figure of Rp62,279,891,076 for the year 2023.

Black hole thermodynamics in natural variables: quadrophenia

It was recently observed in [1] for thermal Kerr-Newman black holes in 4d flat space that one can rewrite the conventional thermodynamics on the inner and outer horizons in terms of left- and right-moving variables with a remarkable simplification of the corresponding expressions. With the goal of illustrating the wide applicability of these newly proposed natural variables, we extend the original observation in four independent directions that can be further superimposed on each other. These four generalizations can be thought of as different deformations of the original 4d Einstein-Maxwell theory, all within the framework of supergravity: higher derivative (HD) corrections in minimal 4d supergravity; additional scalar and vector couplings in matter-coupled 4d supergravity; higher dimensions, in particular 5d minimal supergravity; and a cosmological constant in 4d minimal gauged supergravity with Anti-de Sitter (AdS) vacuum. Each of these generalizations offers a different lesson about the novel thermodynamics, and we pay special attention to the respective BPS limits that can be understood from fixed point formulae, demonstrating the power of the natural variables to capture the full phase space.

Equivariant localization for AdS/CFT

We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity equations. The key ingredient is that supersymmetric AdS solutions with an R-symmetry are equipped with a set of equivariantly closed forms. These may in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline-Vergne-Atiyah-Bott fixed point formula. We illustrate the formalism by considering AdS5 × M6 and AdS3 × M8 solutions of D = 11 supergravity. As well as recovering results for many classes of well-known supergravity solutions, without using any knowledge of their explicit form, we also compute central charges for which explicit supergravity solutions have not been constructed.

Equivariant localization and holography

We discuss the theory of equivariant localization focussing on applications relevant for holography. We consider geometries comprising compact and non-compact toric orbifolds, as well as more general non-compact toric Calabi–Yau singularities. A key object in our constructions is the equivariant volume, for which we describe two methods of evaluation: the Berline–Vergne fixed point formula and the Molien–Weyl formula, supplemented by the Jeffrey–Kirwan prescription. We present two applications in supersymmetric field theories. Firstly, we describe a method for integrating the anomaly polynomial of SCFTs on compact toric orbifolds. Secondly, we discuss equivariant orbifold indices that are expected to play a key role in the computation of supersymmetric partition functions. In the context of supergravity, we propose that the equivariant volume can be used to characterize universally the geometry of a large class of supersymmetric solutions. As an illustration, we employ equivariant localization to prove the factorization in gravitational blocks of various supergravity free energies, recovering previous results as well as obtaining generalizations.

Comparative study on mechanical and environmental properties of coal gangue sand concrete

To reduce the adverse impact of coal gangue heaping and save natural resource, artificial coal gangue sands are utilized as fine aggregates in the concrete preparation. The mechanical and environmental properties of coal gangue sand concrete were studied experimentally and theoretically by considering concrete strength grades (C30, C50) and replacement ratios (0, 25%, 50%, 75%, 100%). The results show that coal gangue sand will weaken the adhesion performance of the transition zone between cement mortar and coarse aggregate. The elastic modulus and axial compressive strength of coal gangue sand concrete were decreased by increasing the replacement ratio regardless of concrete grade. When the replacement ratio is 100%, the elastic modulus and axial compressive strength of C30-grade concrete were reduced by 2.9% and 12.6% respectively whilst the values of C50-grade concrete were 5.0% and 21.5% respectively. Based on the tested results, the prediction formulas of the mechanical properties and the uniaxial compressive stress–strain model of the coal gangue sand concrete under different replacement ratio are proposed. Through life cycle assessment, it is found that the replacement ratio of the coal gangue sand is negatively correlated with environmental impact and willingness to pay (considering transport cost), and positively correlated with willingness to pay (without considering transport cost). The balance point is defined by the environmental influence of coal gangue sand concrete when the willingness to pay (considering transport cost) of coal gangue sand concrete under different replacement ratio is equal. According to the tested results, the prediction formula of the balance point under different transport distance is proposed. When the consistent transportation distance of gangue sand and natural sand exceeds 140 km, the utilization of coal gangue sand can produce good environmental benefits.

Regionalization and optimization strategy of ecological management in Xinjiang, China based on supply-demand relationship and spatial flow of ecosystem services.

As an important basis for the optimization of territorial space, ecological management zoning is of great significance for maintaining regional ecological security and promoting the construction of ecological civilization. With 10 ecosystem services, such as wind break and sand fixation, water conservation, and forest and grass supply, we built a supply index system for Xinjiang. Modelling and ecological economics methods were used to quantify ecosystem service supply. Ecosystem service demand of Xinjiang in 2020 was quantitatively assessed by combining land use intensity, population, and economic status. Based on the ecosystem service supply-demand ratio model and quadrant matching method, we explored the matching relationship and spatial differentiation of ecosystem ser-vice supply and demands on the 1 km grid scale. The breaking point formula and field intensity formula were used to evaluate the flow range and intensity of ecosystem services, and then ecological management zones were divided and corresponding control measures were proposed. The results showed obvious spatial differences in the supply and demand of ecosystem services in Xinjiang in 2020. The high-supply areas were mainly distributed in river valleys and along river systems, while the demand was concentrated in oasis-central cities. The overall supply of ecosystem services was less than the demand. The spatial distribution was dominated by low supply-low demand areas and high supply-high demand areas. There were seven output zones of ecosystem services in Xinjiang, namely Fuyun County, Fuhai County, Yizhou District, Shanshan County, Alashankou City, Keping County and Qira County. The rests were input zones. According to the comprehensive analysis, Xinjiang could be divided into five ecological management areas, i.e., mountain ecological barrier area, oasis ecological restoration area, desert ecological improvement area, desert-oasis ecological protection area, and patch ecological transport area.

Supersymmetric localization: \U0001d4a9 = (2, 2) theories on S2 and AdS2

Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS2, on which we consider an Abelian \U0001d4a9 = (2, 2) theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S2 and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS2 we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS2 as well as S2, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence matches with the perturbative 1-loop evaluation using heat kernel method.

K3 surfaces, Picard numbers and Siegel disks

If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between 0 and 18. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel disks that realize all possible Picard numbers. The constructions involve extensive computer searches for appropriate Salem numbers and computations of algebraic numbers arising from holomorphic Lefschetz-type fixed point formulas and related Grothendieck residues.

Pengaruh Model Pembelajaran ARIAS (Assurance, Relevance, Interest, Assessment, and Satisfaction) dalam Meningkatkan Hasil Belajar IPA Siswa di Sekolah Dasar

This study aims to determine the effect of the ARIAS (Assurance, Relevance, Interest, Assessment, and Satisfaction) learning model on student learning outcomes. Quantitative research using Posttest Only Control Group Design or also known as Quasi Experimental Design. Saturated sampling was used to select 30 students who became research respondents. There were 25 multiple choice questions included in the instrument. The test was used to obtain Posttest value data. Point Biserial correlation formula and reliability calculation will be used to validate the instrument beforehand. With a score of 84.7 the control class performed worse than the experimental class. Data were analyzed by t-test. The t-test results showed that students science learning outcomes increased with the application of the ARIAS learning model in elementary school.

Upper and lower estimations of Popoviciu’s difference via weighted Hadamard inequality with applications

We consider differences coming from Popoviciu?s inequality and give upper and lower bounds by employing weighted Hermite-Hadamard inequality along with the approximations of Montgomery two point formula. We also give bounds for Popoviciu?s inequality by employing weighted Hermite-Hadamard inequality along with the approximations of Montgomery one point formula. We testify this scenario by utilizing the theory of n-times differentiable convex functions. Our results hold for all n ? 2 and we provide explicit examples to show the correctness of the bounds obtained for special cases. Last but not least, we provide applications in information theory by providing new uniform estimations of the generalized Csiszar divergence, Renyi-divergence, Shannon-entropy, Kullback-Leibler divergence, Zipf and Hybrid Zipf-Mandelbrot entropies.

Two point Ostrowski and Ostrowski-Gruss type inequalities on time scales with applications

Here, Fink type identity for two point formula on time scales has been proved, an expansion of Guessab-Schmeisser two points formula for n?times differentiable functions via Fink type identity is established to provide some estimates of Ostrowski and Ostrowski-Gruss type inequalities with applications.

Study on Restoring Force Model of Cold-Formed Thin-Walled Steel Lipped Channel Beam-Columns under Cyclic Load

In order to study the hysteretic behavior and restoring force model of cold-formed thin-walled steel (CFTWS) lipped channel beam-column, a finite element analysis (FEA) model considering the material and geometric nonlinearity and the influence of the initial geometric imperfection under cyclic loading was established by ABAQUS software. Based on the verified FEA model, the hysteretic behavior of CFTWS lipped channel beam-column members with different influencing factors was analyzed by parameterization. The effects of width-to-thickness ratio, axial compression ratio and slenderness ratio on ductility, energy dissipation capacity and stiffness degradation were studied. Based on the results of parameter analysis and the theoretical and regression analysis, the calculation formula of each characteristic point of the trilinear skeleton curve of beam-column member was proposed. Based on the hysteresis curve analysis of beam-column member, the simplified restoring force model (SRFM) of CFTWS lipped channel beam-column was established according to different hysteresis rules for the different buckling modes. The results showed that the SRFM under different buckling modes was in good agreement with the hysteretic curve of FEA, which can better indicate the hysteretic behavior of the member. The proposed SRFM was accurate and applicable, and can provide a fundament for the seismic analysis of the CFTWS lipped channel beam-column.

The decomposition formula for Verlinde Sums

We prove a decomposition formula for Verlinde sums (rational trigonometric sums), as a discrete counterpart to the Boysal-Vergne decomposition formula for Bernoulli series. Motivated by applications to fixed point formulas in Hamiltonian geometry, we develop differential form valued version of Bernoulli series and Verlinde sums, and extend the decomposition formula to this wider context.

An algebraic construction of sum-integral interpolators

This paper presents an algebraic construction of Euler-Maclaurin formulas for polytopes. The formulas obtained generalize and unite the previous lattice point formulas of Morelli and Pommersheim-Thomas, and the Euler-Maclaurin formulas of Berline-Vergne While the approach of this paper originates in the theory of toric varieties, and recovers previous results about characteristic classes of toric varieties, the present paper is self-contained and does not rely on results from toric geometry. We aim in particular to exhibit in a combinatorial way ingredients such as such Todd classes and cycle-level intersections in Chow rings, that first entered the theory of polytopes from algebraic geometry.

Experimental investigations on aviation kerosene Multi-jets in high temperature and low pressure air crossflow

There are the key factors affecting the combustion performance of the burner, including the jet trajectory, fragmentation and evaporation process of fuel jet in air crossflow and the uniform characteristics of fuel-gas mixing. In our experimental investigation, we studied the effects of liquid/air momentum flux ratio, the number of radial and axial injection points on jet trajectory, penetration depth and Sauter mean diameter (SMD) distribution of aviation kerosene injected into high temperature and low pressure air crossflow. Specifically, the pressure of air crossflow was set to 0.06–0.09Mpa, the speed 0.1 Ma, and the temperature 500 K. The jet trajectories of aviation kerosene were captured using a triggered image sensor (CCD) camera; the SMD of the aviation kerosene along the flow direction was measured using a Malvern laser particle sizer. The main observation results are: (1) The liquid/air momentum flux ratio is still the main factor affecting the penetration depth of liquid jet, fitting the dimensionless formula of jet trajectories of aviation kerosene injected into high temperature and low pressure lateral airflow. The fitting formula of single injection point and multiple injection points is y/d=0.4357q0.8384x/d0.4797 and y/d=0.513q0.8869x/d0.3661 respectively. (2) When the air crossflow pressure goes down, it will reduce the aerodynamic Weber number and increase the penetration depth, while it will reduce the Reynolds number of jet liquid and increase the average droplet size. For every 0.01Mpa decrease in air crossflow pressure, the aviation kerosene particle size SMD increases by 5–20 µm. (3) When the number of radial jet points goes up, it will enhance the interaction between CVP (Counter Rotating Vortex Pairs) and complex vortex system between multiple jets, which leads to rising growth rate of jet liquid column surface wave and the premature break-up, reducing the penetration depth by 15–25 mm; Compared with the single injection point, the influence of liquid/air momentum flux ratio on the jet trajectory and penetration depth of the multi-injection point becomes smaller, and the difference is more obvious under the condition of high liquid/air momentum flux ratio.

The Effect of Creativity and Product Innovation on Business Success in Coconut Shell Waste Craftsmen in The Bukit Lawang Plantation Village Bahorok District Langkat Regency

This study aims to determine "The Effect of Creativity and Product Innovation on Business Success in Coconut Shell Waste Craftsmen in the Bukit Lawang Plantation Village, Bahorok District, Langkat Regency". This type of research is associative with a quantitative approach. The population in this study were 30 coconut shell craftsmen using the saturation point formula technique, because the population was less than 100 people, the number of samples in this study was taken absolutely from a population of 30 respondents. Based on the T test and F test, it can be concluded that the creativity and product innovation variables partially have a positive and significant effect on the success of the Coconut Shell Waste Craftsmen in the Bukit Lawang Plantation Village, indicating Ho is rejected and Ha is accepted. Coefficient of Determination (R2) = 0.343 or 34.3%. 65.7% was influenced by other factors not described in this study.

Extended Jensen\u2019s functional for diamond integral via Green\u2019s function and Hermite polynomial

In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension of Jensen’s functional for n-convex functions is deduced from Jensen’s inequality involving diamond integrals. Special Hermite conditions, including Taylor two point formula and Lagrange’s interpolation, are also deployed to find the further extensions of Jensen’s functional. This paper also includes discussion on bounds for Grüss inequality, Ostrowski inequality, and Čebyšev functional associated to the newly defined Jensen’s functional.