This research aims to study the ultimate limit state (ULS) behaviour of stiffened panel under longitudinal compression by non-linear finite element method (NLFEM). There are different types of stiffeners being used in shipbuilding i.e. T-bar, flat-bar and angle-bar. However, this research focuses on the ultimate compressive strength behaviour of flat-bar stiffened panel. A total of 420 of reliable scenarios of flat-bar stiffened panel are selected for numerical simulation by ANSYS NLFEM. The ultimate strength behaviours obtained were used as data for the development of closed form shape empirical formulation. Recently, Kim et al. [1] proposed for advanced empirical formulation for T-bar stiffened panel and the applicability of the proposed formulation to flat-bar stiffened panel will be confirmed by this study. The accuracy of the empirical formulation obtained for flat-bar stiffened panel has been validated by FE simulation results of statistical analysis (R2 = 0.9435). The outcome obtained will be useful for ship structural designers in predicting the ultimate strength performance of flat-bar type stiffened panel under longitudinal compression.

In times of water scarcity, water conservation measures from authorities are primarily directed to the residential sector—homeowners and renters who engage in individual activities to reduce water consumption. Business owners, manufacturers, and institutional workers—the ICI sector, generally, do not receive targeted information and education on water savings measures, and when they do, the information, typically, refers to indoor technologies, and behavior choice. In answer to this shortfall, this research illustrates how the ICI sector might engage in outdoor water conservation and, thus, realize water savings using the well-established Pittenger’s Simplified Landscape Irrigation Design Estimation (SLIDE) formula that estimates outdoor water conservation/savings for the lesser studied industrial, commercial, and institutional (ICI) sector. We applied the SLIDE formula five diverse climate areas in Texas to demonstrate the potential water savings in each, as well as identifying the type of water technology measures that yielded the greatest water savings for outdoor ICI landscapes. Overall, the greatest water savings for outdoor ICI landscapes was realized through smartscape design with soil moisture sensors-SMS technology, second best. Our findings will provide ICI facility owners/managers with knowledge and examples of a simplified system for quantitative decision making when considering choices among technologies and/or practices toward outdoor water conservation for their own facilities.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

Let be a power function $f_{r,M}(s)$ defined for every $s$ within the finite set $M$ as follows $$f_{r,M}(s)= \begin{cases} s^r, \ &s\in M,\\ 0, \ &\mathrm{otherwise}. \end{cases} $$ Let a discrete convolution of $f_{r,M}(s)$ be denoted as follows $\mathrm{Conv}_{r,M}[n]=(f_{r,M}*f_{r,M})[n]$. Let a real coefficients $A_{m,j}$ be given by the following recurrence $$ A_{m,j} = \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \end{cases} $$ In this paper we show that for every $n>0$ the following odd-power identities involving coefficients $A_{m,j}$ and convolution transform $\mathrm{Conv}_{r,M}[n]$ hold $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modelling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature. The model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics). The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation. The model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts. Evidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies Approaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society. Application of the quantum-like model of Frhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and internet based sources.

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

The human ankle is a complex joint, most commonly represented as talocrural and subtalar axes. It is difficult to locate and take in vivo measurements of the ankle joint. There are no instruments for patients lying on a bed or the floor; that can be used in outdoor or remote sites. We have developed a "Turmell-meter" to address these issues. We started with the study of ankle anatomy and anthropometry, then we used the product of exponentials’ formula to visualize the movements. Furthermore, we built a prototype using human proportions and statistics. For pose estimation, we used a trilateration method by applying tetrahedral geometry. Additionally, we computed the axis direction by fitting 3D circles, plotting the manifold and chart as an ankle joint model. We presented the results of simulations, a prototype comprising 45 parts, specifically designed draw-wire sensors, and electronics. Finally, we tested the device by capturing positions and fitting them into the bi-axial ankle model as a Riemannian manifold. The Turmell-meter is intended to be a hardware platform for human ankle joint axis estimation, it is adjustable and has an easy setup. The proposed model has the properties of a chart in a geometric manifold, we provided the details

Nowadays, brain signal processing is performed rapidly in various brain-computer interface (BCI) applications. Most researchers focus on developing new methods for the future or improving the basic implemented models to identify the optimum standalone feature set. Our research focuses on four ideas. One of them introduces future communication models, and the others are for improving old models or methods. These are: 1) new communication imagery model instead of speech imager using the mental task: Due to speech imagery is very difficult, and it is impossible to imagine sound for all of the characters in all of the languages. Our research introduces a new mental task model for all languages that call Lip-sync imagery. This model can use for all characters in all languages. This paper implemented two lip-sync for two sounds, characters or letters. 2) New combination Signals: Selecting an inopportune frequency domain can lead to inefficient feature extraction. Therefore, domain selection is so important for processing. This combination of limited frequency ranges proposes a preliminary for creating Fragmentary Continuous frequency. For the first model, two s intervals of 4 Hz as filter banks were examined and tested. The primary purpose is to identify the combination of filter banks with 4Hz (scale of each filter bank) from the 4Hz to 40Hz frequency domain as new combination signals (8Hz) to obtain well and efficient features using increasing distinctive patterns and decreasing similar patterns of brain activities.3) new supplement bond graph classifier for SVM classifier: When SVM linear uses in very noisy, the performance is decreased. But we introduce a new bond graph linear classifier to supplement SVM linear in noisy data. 4) a deep formula recognition model: it converts the data of the first layer into a formula model (formula extraction model). The main goal is to reduce the noise in the subsequent layers for the coefficients of the formulas. The output of the last layer is the coefficients selected by different functions in different layers. Finally, the classifier extracts the root interval of the formulas, and the diagnosis does based on the root interval. For all of the ideas achieved the results of implementing methods. The results are between 55% to 98%. Less result is 55% for the deep detection formula, and the highest result is 98% for new combination signals.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.