Degree Formula Research Articles

Phase classification and transient effects of the start-up process of multi-functional pump station in pump mode

In the context of achieving the goal of carbon neutrality, multi-functional pump stations (MFPS) have been greatly developed as a new energy system in recent years. The MFPS can operate in forward direction in pump mode to pump water and in turbine mode in reverse direction to generate electricity. At present, the instability of the MFPS during start-up process (SUP) in pump mode has become the key to restricting the operating life and further development of MFPS. In this paper, based on the motion characteristics of the pump and the cut-off facility (COF), the SUP of the MFPS in pump mode is clearly classified. In order to reveal the transient effect during the SUP, the steady-state full characteristic experiment (SFCE) of the pump was carried out. The occurrence phase of the transient effect during the SUP is analyzed, and the deviation between the steady-state external characteristics and the transient characteristics is revealed. In this study, the evaluation formula of the start-up completion degree (SUCD) of the MFPS in pump mode is proposed for the first time, and the evaluation and identification of the start-up progress at different phases are completed. The results show that the water flow in the system is in a reverse flow state in the Phase I. The SUCD of Phase I is 17 %. In the Phase II, The high-speed jet flow in the pump flows to the inlet of the guide vane (GV), which gradually changes the mainstream direction in the GV. A certain vortex structure can be observed at the exit of the flap gate (FG). The SUCD of Phase II is 61 %. In the Phase I and II, the dimensionless head of transient simulation is much larger than that of SFCE. In the Phase III, the flow state in the impeller will gradually stabilize. The transient effect disappears and the pressure fluctuation intensity decreases. The SUCD of Phase III is 93 %. In the Phase IV, the separation vortex that persists from Phase I-III at the tail of the GV blades disappears. The diversion capacity at the gate increases, and significant annular flow can be observed near the FG.

Optimal Design of Formulas for a Single Degree of Freedom Tuned Mass Damper Parameter Using a Genetic Algorithm and H2 Norm.

One of the researchers' concerns in structural engineering is to control the dynamic behavior of structures efficiently. The TMD (tuned mass damper) is one of the effective methods of controlling the vibration of structures, and various numerical techniques have been proposed to find the optimal parameters of the TMD. This paper develops a new explicit formula to derive the optimal parameters of the TMD of a single degree of freedom (SDOF) structure under seismic load using a genetic algorithm (GA). In addition, the state-space model and the H2 norm function are used to identify the optimal frequency ratio and damping ratio of the TMD that minimize the overall vibration energy of the structure. The MATLAB curve fitting toolbox is used for the explicit formula proposal, and the validity of the proposed formula is verified through multidimensional performance verification technique. Finally, the TMD parameters of the SDOF structure are applied to the multi-degrees of freedom (MDOF) structure to compare and analyze with the existing research results, and the results of the explicit formula proposed in this paper are confirmed to be excellent. This paper can suggest a new direction for determining the optimal TMD parameters using a GA and can be effectively applied to vibration control problems of various structures.

Characters of [formula omitted] and vertex operators

In this paper, we present a vertex operator approach to construct and compute all complex irreducible characters of the general linear group GLn(Fq). Green's theory of GLn(Fq) is recovered and enhanced under the realization of the Grothendieck ring of representations RG=⨁n≥0R(GLn(Fq)) as two isomorphic Fock spaces associated to two infinite-dimensional F-equivariant Heisenberg Lie algebras hˆF‾ˆq and hˆF‾q, where F is the Frobenius automorphism of the algebraically closed field F‾q. Under this picture, the irreducible characters are realized by the Bernstein vertex operators for Schur functions, the characteristic functions of the conjugacy classes are realized by the vertex operators for the Hall-Littlewood functions, and the character table is completely given by matrix coefficients of vertex operators of these two types. One of the features of the current approach is a simpler identification of the Fock space RG as the Hall algebra of symmetric functions via vertex operator calculus, and another is that we are able to compute in general the character table, where Green's degree formula is demonstrated as an example.

Reinforcements/matrix micro-interface evolution and properties of in-situ Ni60A/WC coatings prepared by laser cladding

Ni60A/WC in-situ reinforced composite coatings are prepared on Inconel 718 alloy by laser cladding. The reinforcements/matrix micro-interface evolution, microhardness, and corrosion resistance are investigated. The phases in the coatings are mainly composed of γ-Ni, M23C6, M7C3 and NbC. The reinforcements/matrix micro-interfaces concerned in the coatings mainly include WC/matrix micro-interface and M23C6/matrix micro-interface. The WC/matrix micro-interface evolution is divided into five stages, namely, WC enters the molten pool, the micro-interface begins to grow, the reinforcements enriched at the tip, the reinforcements fall off and the formation of the stable micro-interface. The microhardness of the coatings increases with increasing WC content. On one hand, the increase in WC content promotes the generation of in-situ reinforcements, and the large lattice mismatch between dispersed reinforcement particles and matrix hinders dislocation motion. On the other hand, the two-dimensional mismatch degree of WC and γ-matrix calculated by Bramfitt's two-dimensional mismatch degree formula is 9.77 %, indicating that WC particles can serve as particles for γ heterogeneous nucleation. The increase of WC particles plays the role of fine grain strengthening, so the microhardness of the coating increases. The effect of WC on the corrosion resistance is also analyzed. The reinforcements are mainly distributed in the grain boundaries, and the HRTEM results indicate that a large degree of lattice mismatch exists in the micro-interface of reinforcements and γ-matrix. The large degree of mismatch shows that the interface between the two phases is relatively weak, and the weak interface is easy to become the channel for corrosive ion (Cl−) diffusion.

Formal degree of regular supercuspidals

Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its L -parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha’s regular supercuspidal L -packets satisfy the conjecture.

Subpolygroup commutativity degree of finite extension polygroup

In this paper, we consider finite extension polygroups as a special class of polygroups to study probabilistic polygroup theory. In this regard, we study the subpolygroup lattice of the extension polygroups. By using the results of the subpolygroup lattice, we obtain an explicit formula for the subpolygroup commutativity degree of the extension polygroup.

Characteristics of life space remodelling in tourism-based villages during rural gentrification based on the coupled coordination degree model

Abstract This paper first takes the process of rural gentrification as the main line, selects the village of Annoyed bun in Hohhot City, Inner Mongolia Province, as the case area, conducts research on the characteristics of the remodeling of the living space of the village of the annoyed bun, and proposes the theoretical system of rural gentrification, the governance structure and the mechanism. Secondly, the research on tourism-based villages based on the coupling coordination degree model is carried out to determine the evaluation factors in the coupling index system of tourism-based villages according to the needs of tourists and then construct the evaluation index system of the coupling coordination degree model. Then, the entropy value method is used to calculate the weight of each index, and on the result of the weight of each index, the coupling coordination degree formula can be used to derive the comprehensive evaluation index and the fusion coordination degree value, and then analyze the example of the tourism-type village based on the coupling coordination degree model. The results show that on the value of the degree of integration and coordination, in the three years from 2015 to 2017, Hohhot City, Hohhot City, annoying package village ecology and tourism-type villages mainly show the role of mutual promotion, Hohhot City, towards the direction of mutual promotion between the two. This study promotes the revitalization, reconstruction and reorganization of village life, which objectively becomes a new path for constructing new rural areas and rejuvenation in China.

Second-order coherence and polarization characteristics of partially coherent radially polarized cosh-Gaussian vortex beams in a turbulent atmosphere

The second-order coherence and polarization characteristics of partially coherent radially polarized cosh-Gaussian vortex (PCRPChGV) beams in atmospheric turbulence are investigated based on the extended Huygens–Fresnel principle. The analytical propagation formulas of cross-spectral density matrix, average intensity and degree of polarization (DOP) for PCRPChGV beams in turbulence are derived. The influences of initial correlation length, cosh factor and turbulence intensity on average intensity, on-axis intensity and DOP of PCRPChGV beams are examined numerically. Results show that with increasing propagation distance, the PCRPChGV beam evolves from the initially separated double-lobe spot into overlapping double-lobe spot, and Gaussian spot. The corresponding intensities of the two Cartesian components of light field rotate markedly around the beam axis in a unique manner. Initial correlation length and cosh factor have an obvious influence on the position and size of normalized on-axis intensity peak, respectively. In addition, PCRPChGV beams in moderate turbulence have strong anti-turbulence ability.

Compaction quality evaluation method based on dual-index in intelligent compaction of filling foundation

The compaction quality evaluation of soils, as the essence of intelligent compaction (IC) technology, is a key issue for controlling the construction quality of infrastructure such as airports, dams, and roads. However, the commonly used compaction quality evaluation methods often only adopt a single index involving compaction times or acceleration amplitude which could be prone to misjudging the compaction quality of soils, resulting in difficulties in ensuring the validity of the compaction quality evaluation. To solve the abovementioned problem, a novel compaction quality evaluation method based on dual-index in IC is proposed. Firstly, the relationship between the basic variables in the single-index compaction quality evaluation methods and the causes of the associated misjudgment are explained. Then, the formula of the compaction degree of soils based on the proposed method is given. Next, a determination method of the optimal weight factors in the proposed calculation formula is introduced in detail. Finally, the capability and performance of the proposed method are validated through theoretical analysis and relevant case studies. The results indicate that the proposed dual-index compaction quality evaluation method can effectively reduce the misjudgment probability of compaction quality of soils compared to the single-index compaction quality evaluation method. Moreover, the compaction degree determined by the proposed method shows a better agreement with the real compaction degree of soils, demonstrating that the proposed method provides an effective tool for IC process control and management.

Research on Safety Evaluation and System Development of Tunnel Lining Based on Set Pair Analysis

Considering the importance of lining thickness in lining safety, and realizing the synchronization of safety evaluation and information development, this paper combines the methods of literature research and field investigation, focuses on six influencing factors, such as the deterioration of lining materials, the deformation of lining and the lack of tunnel clearance, et al. An evaluation index system of structural safety classification is established, and then substantiates each index and defines its quantitative or qualitative evaluation criteria. Through the normalization processing, the state of the evaluation index can be characterized by the normalized value. Analysing the characteristics, structure, relationship, trend and the mode of their mutual connection between the indexes by set pair analysis method, the calculation formula of the connection degree is obtained, and then the set pair potential vector is obtained. According to the principle of maximum set pair potential, the safety evaluation of lining structure is divided into five levels: safe, safer, less safe, unsafe and extremely unsafe. With the help of App Designer tool in MATLAB software, a program suitable for lining safety evaluation is designed and developed independently. Combined with a tunnel project in Chongqing, the above method is used to judge the lining safety of the tunnel project in order to provide a quick way for tunnel safety evaluation.

On the properties of some inversion methods of the Laplace transform

The problem of inversion of the integral Laplace transform, which belongs to the class of ill-posed problems, is considered. Integral equations are reduced to ill-conditioned systems of linear algebraic equations, in which the unknowns are either the coefficients of the series expansion in terms of special functions, or the approximate values of the desired original at a number of points. Described method of inversion using special quadrature formulas of the highest degree of accuracy and the characteristics of the accuracy and stability of this method are indicated. Quadrature inversion formulas are constructed, which are adapted for the inversion of long-term and slow processes of linear viscoelasticity. A method of deformation of the integration contour in the Riemann-Mellin inversion formula is proposed, which leads the problem to the calculation of certain integrals and allows obtaining error estimates. A method is described for determining the possible breakpoints of the original and calculating the magnitude of the jump at these points.

Energy and Wiener index of divisor graph of commutative ring

In recent paper, P. D. Khandare et al. introduced a graphical structure of non empty finite ring R called as divisor graph ⅅ[R] and discussed some properties of the graph ⅅ[Zn]. In this article, we will continue the study of the divisor graph ⅅ[Zn] and discuss some more properties of ⅅ[Zn]. If n ∈ N then we derive general formula for total degree and stability number of ⅅ[Zn]. Moreover we find adjacency matrix of the graph ⅅ[Zn] and derived formula for energy of ⅅ[Zn] when n = pk, k ∈ N and n = pq, for primes p and q.

On subpolygroup commutativity degree of finite polygroups

<abstract><p>Probabilistic group theory is concerned with the probability of group elements or group subgroups satisfying certain conditions. On the other hand, a polygroup is a generalization of a group and a special case of a hypergroup. This paper generalizes probabilistic group theory to probabilistic polygroup theory. In this regard, we extend the concept of the subgroup commutativity degree of a finite group to the subpolygroup commutativity degree of a finite polygroup $ P $. The latter measures the probability of two random subpolygroups $ H, K $ of $ P $ commuting (i.e., $ HK = KH $). First, using the subgroup commutativity table and the subpolygroup commutativity table, we present some results related to the new defined concept for groups and for polygroups. We then consider the special case of a polygroup associated to a group. We study the subpolygroup lattice and relate this to the subgroup lattice of the base group; this includes deriving an explicit formula for the subpolygroup commutativity degree in terms of the subgroup commutativity degree. Finally, we illustrate our results via non-trivial examples by applying the formulas that we prove to the associated polygroups of some well-known groups such as the dihedral group and the symmetric group.</p></abstract>

A degree formula for equivariant cohomology rings

A degree formula for equivariant cohomology rings

Group decision‐making analysis based on distance measures under rough environment

AbstractA rough set as a superset of a crisp set is a mathematical tool to cope with uncertainty using initial data without additional assumptions and pre‐defined parameters. Using the technique of upper and lower approximations, rough models provide a complete description of the problem. This paper aims to introduce the notion of distance function, which is a metric, in rough graphs. We establish formulae of distance function, degree and radius of certain products of rough graphs in terms of initial given rough graphs. We discuss the concepts of weak isomorphism and isomorphism in rough graphs, and describe the properties of isomorphic rough graphs. We demonstrate the significance and importance of the distance function with an application to a decision making problem concerning organ trafficking networks. An application of rough matrices in steam valve systems is discussed, and we show how they can help to identify the potential failures and risk components during the power generation process. The results obtained under the rough model are compared with existing extensions of graphs and fuzzy based approaches.

Castelnuovo-Mumford regularity of ladder determinantal varieties and patches of Grassmannian Schubert varieties

We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and 1432-avoiding permutations via tableau combinatorics. These formulas generalize a formula for degrees of symmetric Grothendieck polynomials which appeared in previous joint work of the authors with Y. Ren and A. St. Dizier.We apply our formulas to compute Castelnuovo-Mumford regularity of classes of generalized determinantal ideals. In particular, we give combinatorial formulas for the regularities of all one-sided mixed ladder determinantal ideals. We also derive formulas for the regularities of certain Kazhdan-Lusztig ideals, including those coming from open patches of Schubert varieties in Grassmannians. This provides a correction to a conjecture of Kummini-Lakshmibai-Sastry-Seshadri (2015).

CAREER CHOICE OF BUILDING ENGINEERING EDUCATION ALUMNI OF PALANGKA RAYA UNIVERSITY

Career choice is the determination of a career that affects a person's position, where the determination is influenced by several factors either internal factors or from the individual or external or from outside the individual for the sake of progress and survival. This research aims to find out: 1. what percentage of alumni career choices in the field of education, non-education but related to Building Technology and not both 2. whether alumni career options fit the profile of graduates 3. or the curriculum has significantly affected alumni careers. This research is a descriptive study with a quantitative approach, the subject of this study is an alumniof Building Engineering Education of Palangka Raya University in June 2021 with a population of 83 alumni and a sample number of 40 alumni. Questionnaires on the likert scale are used as instruments to collect the necessary data, these questionnaires are created in the form of google forms and distributed online to alumni. Then, the data is analyzed using the achievement degree formula (DP). The results showed that the highest percentage of consecutive career choices, not educators and not related to the field of building engineering science (62.5%), not educators but still related to the field of building engineering (22.5%) and educators (15%). And alumni students who choose a career according to the graduate profile of the Building Engineering Education study program curriculum by (37.5%) and the non-conforming (62.5%). So it can be concluded that most of the alumni of Building Engineering Education students in their career selection do not match the profile of graduates of the curriculum of the Building Engineering Education Study Program of Palangka Raya University. While the average percentage of the influence of the Building Engineering Education curriculum on alumni in a career is 73.18% and belongs to the category quite well. This shows that the curriculum of Building Engineering Education is significantly quite good in influencing alumni in a career

Some classical analysis results for continuous definable mappings

In this paper, we show that some fundamental results for smooth mappings (e.g., the Brouwer degree formula, the implicit function and inverse function theorems, the mean value theorem, Sard's theorem, Hadamard's global invertibility criteria, Pourciau's surjectivity and openness results) have natural extensions for continuous mappings that are definable in o-minimal structures. The arguments rely on nice properties of definable mappings and sets.

On the Base Point Locus of Surface Parametrizations: Formulas and Consequences

This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant. As a consequence, we get a new proof of the degree formula relating the degree of the surface, the degree of the parametrization, the base point multiplicity and the degree of the rational map induced by the parametrization. In addition, we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related. As an application of these results, we explore how the degree of a surface reparametrization is affected by the presence of base points.

Relative g-noncommuting graph of finite groups

Let G be a finite group. For a fixed element g in G and a given subgroup H of G , the relative g -noncommuting graph of G is a simple undirected graph whose vertex set is G and two vertices x and y are adjacent if x ∈ H or y ∈ H and [ x , y ]≠ g , g −1 . We denote this graph by Γ H , G g . In this paper, we obtain computing formulae for degree of any vertex in Γ H , G g and characterize whether Γ H , G g is a tree, star graph, lollipop or a complete graph together with some properties of Γ H , G g involving isomorphism of graphs. We also present certain relations between the number of edges in Γ H , G g and certain generalized commuting probabilities of G which give some computing formulae for the number of edges in Γ H , G g . Finally, we conclude this paper by deriving some bounds for the number of edges in Γ H , G g .