Mathematical model in the banking on the ex ample of simple percentage

Mathematical modeling is the description of the reality in the language of the mathematics and formal logic which creates symbols, mathematical relation and also strictly determined rules of employing them (Jaworski, Micał 2005). This article is devoted to the structure of the model describing the process of increasing the capital value within the time which basis constitutes the calculations based on the rule of simple percentage. In its content are determined the chosen, basic terms associated with the financial activity of the bank (including interest rate, interest, discount). Mathematical models are also discussed enabling to count: the final capital for the initial capital with the fixed annual interest rate for the set time, the initial capital which generated the determined final capital with the fixed annual interest rate for the set time, the interest rate on the basis of the initial and final capital after certain time, the initial value of the loan for the amount of the payoff within the fixed discount rate within the certain time, the value of the commercial discount for one year on the basis of the initial value of the loan and the amount of its payoff. The presented content will supply the reader with the knowledge in calculations applied in the banks associated with the simple percentage. The article constitutes the example of combination of the theoretical knowledge with the practice and it also shows how important mathematical modeling is in the modern world.

Mathematical Relation between Concurrence and Intensity of a Photon in the Quantum Delayed-Choice Experiment

I provide the explicit mathematical expression of the correlation between concurrence and the intensity of a photon in the quantum delayed-choice experiment. This shows us that one may observe the wave-particle duality and entanglement simultaneously.

A mathematical model of relation and origin of variation between CRI and CSR indexes

The aim of this work is both the mathematical relation and the value variation analysis between CRI and CSR indexes. For this aim the physical mathematical model is proposed on the basis of the ISO-test. The physical basis of the model is a material balance of a one piece of coke from the ISO sample. Results of calculating by the model are curves of CSR=f(CRI) which reproduces the regressions in analogy with CSR=a+b.CRI for most coke-producing countries. The model showed that a larger part of CSR=f(CRI) curve is linear and that a universal regression in analogy with CSR=a+b.CRI does not exist. As follows from the model, every piece of coke from the ISO sample has its own CSR=f(CRI) curve with a CRI and CSR point. Between pieces of coke, variations of CRI and CSR values can be explained by the open pore amount, the coke pores’ surface area, the statistical distribution of molecular oriented domains on the basis of Lc and the coke piece mass. In our results, pores with a geometrical orientation from the outside to the center of a coke piece and having a minimum length significantly influence on the coke quality according to CRI and CSR indexes.

Predicting the Parameters of Vortex Bladeless Wind Turbine Using Deep Learning Method of Long Short-Term Memory

From conventional turbines to cutting-edge bladeless turbines, energy harvesting from wind has been well explored by researchers for more than a century. The vortex bladeless wind turbine (VBT) is considered an advanced design that alternatively harvests energy from oscillation. This research investigates enhancing the output electrical power of VBT through simulation of the fluid–solid interactions (FSI), leading to a comprehensive dataset for predicting procedure and optimal design. Hence, the long short-term memory (LSTM) method, due to its time-series prediction accuracy, is proposed to model the power of VBT from the collected data. To find the relationship between the parameters and the variables used in this research, a correlation matrix is further presented. According to the value of 0.3 for the root mean square error (RMSE), a comparative analysis between the simulation results and their predictions indicates that the LSTM method is suitable for modeling. Furthermore, the LSTM method has significantly reduced the computation time so that the prediction time of desired values has been reduced from an average of two and a half hours to two minutes. In addition, one of the most important achievements of this study is to suggest a mathematical relation of output power, which helps to extend it in different sizes of VBT with a high range of parameter variations.

Complementarity principle in terms of electron density for the study of EGFR complexes

The complementarity principle is a well-established concept in the field of chemistry and biology. This concept is widely studied as the lock-and-key relationship between two structures, such as enzyme and ligand interactions. These interactions are based on the overlap of electron clouds between two structures. In this study, a mathematical relation determining complementarity of intermolecular contacts in terms of overlaps of electron clouds was examined using a quantum orbital-free AlteQ method developed in-house for 64 EGFR–ligand complexes with experimentally measured binding affinity data. A very high correlation was found between the overlap of ligand and enzyme electron clouds and the calculated terms, providing a good basis for prognosis of bioactivity and for molecular docking studies.

Investigation on the Mathematical Relation Model of Structural Reliability and Structural Robustness

Structural reliability and structural robustness, from different research fields, are usually employed for the evaluative analysis of building and civil engineering structures. Structural reliability has been widely used for structural analysis and optimization design, while structural robustness is still in rapid development. Several dimensionless evaluation indexes have been defined for structural robustness so far, such as the structural reliability-based redundancy index. However, these different evaluation indexes are usually based on subjective definitions, and they are also difficult to put into engineering practice. The mathematical relational model between structural reliability and structural robustness has not been established yet. This paper is a quantitative study, focusing on the mathematical relation between structural reliability and structural robustness so as to further develop the theory of structural robustness. A strain energy evaluation index for structural robustness is introduced firstly by considering the energy principle. The mathematical relation model of structural reliability and structural robustness is then derived followed by a further comparative study on sensitivity, structural damage, and random variation factor. A cantilever beam and a truss beam are also presented as two case studies. In this study, a parabolic curve mathematical model between structural reliability and structural robustness is established. A significant variation trend for their sensitivities is also observed. The complex interaction mechanism of the joint effect of structural damage and random variation factor is also reflected. With consideration of the variation trend of the structural reliability index that is affected by different degrees of structural damage (mild impairment, moderate impairment, and severe impairment), a three-stage framework for structural life-cycle maintenance management is also proposed. This study can help us gain a better understanding of structural robustness and structural reliability. Some practical references are also provided for the better decision-making of maintenance and management departments.

Theoretical Analysis of a Mathematical Relation between Driving Pressures in Membrane-Based Desalting Processes

Osmotic and hydraulic pressures are both indispensable for operating membrane-based desalting processes, such as forward osmosis (FO), pressure-retarded osmosis (PRO), and reverse osmosis (RO). However, a clear relation between these driving pressures has not thus far been identified; hence, the effect of change in driving pressures on systems has not yet been sufficiently analyzed. In this context, this study formulates an actual mathematical relation between the driving pressures of membrane-based desalting processes by taking into consideration the presence of energy loss in each driving pressure. To do so, this study defines the pseudo-driving pressures representing the water transport direction of a system and the similarity coefficients that quantify the energy conservation rule. Consequently, this study finds three other theoretical constraints that are required to operate membrane-based desalting processes. Furthermore, along with the features of the similarity coefficients, this study diagnoses the commercial advantage of RO over FO/PRO and suggests desirable optimization sequences applicable to each process. Since this study provides researchers with guidelines regarding optimization sequences between membrane parameters and operational parameters for membrane-based desalting processes, it is expected that detailed optimization strategies for the processes could be established.

ESTIMATION OF TIDAL EXCURSION LENGTH ALONG THE SHATT AL-ARAB ESTUARY, SOUTHERN IRAQ

The tidal excursion length along the Shatt Al-Arab estuary was estimated based on the mathematical relation proposed by Parsa and Shahidi (2010). The field measurements of water level, bathymetry, and discharges were conducted to fulfill the objective of the study. The results revealed that the tidal excursion length is site-specific and depends on the characteristics of location which include tidal phases, bathymetry, and geometry. However, the results indicated that there are pronounced differences in tidal excursions lengths between the spring and neap tide phases in all studies stations. The spring tide coincided with the maximum tidal excursion lengths in Shatt Al-Arab estuary with 16.537, 16.187, 11.122, and 9.139 km in the estuary mouth, Faw, Siba, and Abo Flous stations respectively. While the neap tidal excursion lengths were 12.298, 9.254, and 7.269 km in Faw, Siba, and Abo Flous stations respectively.

Analysis of the application of ideal gas equation of state

In nature, the molecules of real gas have a certain volume and have interaction force with each other. It is difficult to find the molecular motion law of real gas because of its complex properties. An ideal gas is an imaginary substance that does not exist in reality. Its molecules are elastic, non volume particles, and there is no interaction among them. This kind of gas is simple in nature and easy to be analyzed and calculated by simple mathematical relation. The introduction of the concept of ideal gas greatly simplifies the analysis of some thermodynamic problems.

Peculiarities of quasicrystalline films formation processes on crystal surface under irradiation with proton-ion flows

Quasicrystalline film with densest package of atoms can be formed on a crystal surface under irradiating crystal surface with protonion flows at a certain ratio of atoms diameters of irradiated crystal and the ions of irradiating flow. Atom-free area of 1 Å order is formed. These are traps for protons from the irradiation stream, thus a quantum dot appears. Atomic package of quasicrystalline film is a package of equilateral Penrose rhombs and there are centers of atoms mass at the vertices. A mathematical relation is obtained that allows predicting radii of irradiation flux ions to form quasicrystalline film and select atomic composition of the obtained film with predetermined properties. Nanostructuring of materials is an entire family of physicochemical processes associated with proton transfer and their localization in crystal lattice and these include ion exchange, diffusion, and ion implantation. Ion and proton exchange can be considered an established universal method of surface modification technology [24– 26]. The case of implantation of protons into the structure of cluster systems formed on the surface of crystals is described in this paper. In this case, a quantum dot is formed in the cluster structure, which is a potential hole with quantized proton motion, wherein the radiation of quantum dot is in IR area of electromagnetic spectrum.