A Node Placement Algorithm Utilizing Mobile Nodes in WSN and IoT Networks

The operation of the Internet of Things (IoT) networks and Wireless Sensor Networks (WSN) is often disrupted by a number of problems, such as path disconnections, network segmentation, node faults, and security attacks. A method that gains momentum in resolving some of those issues is the use of mobile nodes or nodes deployed by mobile robots. The use of mobile elements essentially increases the resources and the capacity of the network. In this work, we present a Node Placement Algorithm with two variations, which utilizes mobile nodes for the creation of alternative paths from source to sink. The first variation employs mobile nodes that create locally-significant alternative paths leading to the sink. The second variation employs mobile nodes that create completely individual (disjoint) paths to the sink. We then extend the local variation of the algorithm by also accounting for the energy levels of the nodes as a contributing factor regarding the creation of alternative paths. We offer both a high-level description of the concept and also detailed algorithmic solutions. The evaluation of the solutions was performed in a case study of resolving congestion in the network. Results have shown that the proposed algorithms can significantly contribute to the alleviation of the problem of congestion in IoT and WSNs and can easily be used for other types of network problems.

A Mechanistic Study on the Formation of Dronic Acids

Dronic acid derivatives, important drugs against bone diseases, may be synthesized from the corresponding substituted acetic acid either by reaction with phosphorus trichloride in methanesulfonic acid as the solvent or by using also phosphorous acid as the P-reactant if sulfolane is applied as the medium. The energetics of the two protocols were evaluated by high-level quantum chemical calculations on the formation of fenidronic acid and benzidronic acid. The second option, involving (HO)2P‑O‑PCl2 as the nucleophile, was found to be more favorable over the first variation, comprising Cl2P‑O‑SO2Me as the real reagent, especially for the case of benzidronate.

Analysis and evaluation of the effect of reflectance values on internal walls, internal roofs, and light shelf on optimal illumination levels in the diploma economics and business building of the vocational school UGM, Yogyakarta

The use of natural light as a source of lighting in buildings is an option in energy saving. One of the efforts that has been made is the installation of a light shelf. The light shelf installed in the UGM Vocational School Economics and Business Diploma (DEB SV) building is not fully working optimally. As many as 83% of the light shelf in lecture rooms is covered by curtains because it is considered to produce excess light (glare). This results in a greater consumption of lighting electricity. This study was conducted to analyze and evaluate the effect of the reflectance value (color) attached to the internal walls, internal roof, external light shelf, and internal light shelf on the indicator of illumination levels Useful Daylight Illuminance (UDI). Furthermore, this study aims to determine the optimum reflectance value (color) parameter. The research was conducted with a simulation method using RadianceIES in the IESVE 2021 software. The first simulation results show the value of reflectance (color) installed (base case) on the internal wall, internal roof, external light shelf, and internal light shelf in one of the lecture rooms of the DEB SV UGM building resulting in a very large value of the UDI>2000lux indicator, which is 84,9% (not according to the criteria). The results of the second simulation provide two variations of the optimum reflectance (color) parameters in the independent variable. The first variation is the internal walls, internal roof, external light shelf, and internal light shelf, each of which has a reflectance value (color) of 90,67% (beige), 100% (white), 90,67% (beige), and 100% (white). The second variation is the internal walls, internal roof, exte rnal light shelf, and internal light shelf, each of which has a reflectance value (color) of 90,67% (beige), 100% (white), 90,67% (beige), and 90,67% (beige).

On the heat content functional and its critical domains

We study and classify smooth bounded domains in an analytic Riemannian manifold which are critical for the heat content at all times $$t>0$$ t > 0 . We do that by first computing the first variation of the heat content, and then showing that $$\Omega $$ Ω is critical if and only if it has the so-called constant flow property, so that we can use a previous classification result established in [33] and [34]. The outcome is that $$\Omega $$ Ω is critical for the heat content at time t, for all $$t>0$$ t > 0 , if and only if $$\Omega $$ Ω admits an isoparametric foliation, that is, a foliation whose leaves are all parallel to the boundary and have constant mean curvature. Then, we consider the sequence of functionals given by the exit-time moments $$T_1(\Omega ),T_2(\Omega ),\dots $$ T 1 ( Ω ) , T 2 ( Ω ) , ⋯ , which generalize the torsional rigidity $$T_1$$ T 1 . We prove that $$\Omega $$ Ω is critical for all $$T_k$$ T k if and only if $$\Omega $$ Ω is critical for the heat content at every time t, and then we get a classification as well. The main purpose of the paper is to understand the variational properties of general isoparametric foliations and their role in PDE’s theory; in some respects they generalize the properties of the foliation of $$\mathbf{R}^{n}$$ R n by Euclidean spheres.

On the Stability Problem of Equilibrium Discrete Planar Curves

We study planar polygonal curves with the variational methods. We show a unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first variation of the length functional. Moreover, we determine the equilibrium curves for the length functional under the area-constraint condition and study their stability.

Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition LkHk+1 = λHk+1

In this paper, we try to give a classification of spacelike hypersurfaces of the Lorentz-Minkowski space-time E1n+1, whose mean curvature vector field of order (k+ 1) is an eigenvector of the kth linearized operator Lk, for a non-negative integer k less than n. The operator Lk is defined as the linear part of the first variation of the (k + 1)th mean curvature of a hypersurface arising from its normal variations. We show that any spacelike hypersurface of E1n+1 satisfying the condition LkHk+1 = λHk+1 (where 0 ≤ k ≤ n − 1) belongs to the class of Lk-biharmonic, Lk-1-type or Lk-null-2-type hypersurface. Furthermore, we study the above condition on a well-known family of spacelike hypersurfaces of Lorentz-Minkowski spaces, named the weakly convex hypersurfaces (i.e. on which all of principle curvatures are nonnegative). We prove that, on any weakly convex spacelike hypersurface satisfying the above condition for an integer k (where, 0 ≤ r ≤ n−1), the (k + 1)th mean curvature will be constant. As an interesting result, any weakly convex spacelike hypersurfaces, having assumed to be Lk-biharmonic, has to be k-maximal.

Pansu–Wulff shapes in ℍ1

We consider an asymmetric left-invariant norm ∥ ⋅ ∥ K {\|\cdot\|_{K}} in the first Heisenberg group ℍ 1 {\mathbb{H}^{1}} induced by a convex body K ⊂ ℝ 2 {K\subset\mathbb{R}^{2}} containing the origin in its interior. Associated to ∥ ⋅ ∥ K {\|\cdot\|_{K}} there is a perimeter functional, that coincides with the classical sub-Riemannian perimeter in case K is the closed unit disk centered at the origin of ℝ 2 {{\mathbb{R}}^{2}} . Under the assumption that K has C 2 {C^{2}} boundary with strictly positive geodesic curvature we compute the first variation formula of perimeter for sets with C 2 {C^{2}} boundary. The localization of the variational formula in the non-singular part of the boundary, composed of the points where the tangent plane is not horizontal, allows us to define a mean curvature function H K {H_{K}} out of the singular set. In the case of non-vanishing mean curvature, the condition that H K {H_{K}} be constant implies that the non-singular portion of the boundary is foliated by horizontal liftings of translations of ∂ ⁡ K {\partial K} dilated by a factor of 1 H K {\frac{1}{H_{K}}} . Based on this we can define a sphere 𝕊 K {\mathbb{S}_{K}} with constant mean curvature 1 by considering the union of all horizontal liftings of ∂ ⁡ K {\partial K} starting from ( 0 , 0 , 0 ) {(0,0,0)} until they meet again in a point of the vertical axis. We give some geometric properties of this sphere and, moreover, we prove that, up to non-homogeneous dilations and left-translations, they are the only solutions of the sub-Finsler isoperimetric problem in a restricted class of sets.

Machine Intelligence-Based Trend Analysis of COVID-19 for Total Daily Confirmed Cases in Asia and Africa

COVID-19 is likely to pose a significant threat to healthcare, especially for disadvantaged populations due to the inadequate condition of public health services with people's lack of financial ways to obtain healthcare. The primary intention of such research was to investigate trend analysis for total daily confirmed cases with new corona virus (i.e., COVID-19) in the countries of Africa and Asia. The study utilized the daily recorded time series observed for two weeks (52 observations) in which the data is obtained from the world health organization (WHO) and world meter website. Univariate ARIMA models were employed. STATA 14.2 and Minitab 14 statistical software were used for the analysis at 5% significance level for testing hypothesis. Throughout time frame studied, because all four series are non-stationary at level, they became static after the first variation. The result revealed the appropriate time series model (ARIMA) for Ethiopia, Pakistan, India, and Nigeria were Moving Average order 2, ARIMA(1, 1, 1), ARIMA(2, 1, 1), and ARIMA (1, 1, 2), respectively.

Regularized Asymptotic Solutions of Integro-Differential Equations with Fast and Slow Variables

The article considers a nonlinear integro-differential system of equations with fast and slow variables. Such systems were not considered previously from the point of view of constructing regularized (according to Lomov) asymptotic solutions. The known studies were mainly devoted to construction of the asymptotics of the Butuzov-Vasil'eva boundary layer type, which, as is known, can be applied only if the spectrum of the first variation matrix (on the degenerate solution) is located strictly in the open left-half plane of a complex variable. If the spectrum of this matrix falls on the imaginary axis, the S.A. Lomov regularization method is commonly used. However, this method was mainly developed for singularly perturbed differential systems that do not contain integral terms, or for integro-differential problems without slow variables. In this article, the regularization method is generalized for two-dimensional integro-differential equations with fast and slow variables.

A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space

We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries.