Nondegenerate Spheres in Four Dimensions by Do, Thao

“…A $$\beta $$ β -nondegenerate graph can have up to $$\Theta (|P||Q|)$$ Θ ( | P | | Q | ) edges without any restriction, but must have much fewer edges if the graph is semi-algebraic or has bounded VC-dimension. We show that Elekes–Tóth’s bound for nondegenerate hyperplanes, Apfelbaum–Sharir’s bound for nondegenerate spheres in  $$\mathbb {R}^3$$ R 3 , and our new bound for nondegenerate spheres in  $$\mathbb {R}^4$$ R 4 , all hold under this new definition.…”
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Three-dimensional solitary waves in dispersive wave systems by Kim, Boguk, Ph. D. Massachusetts Institute of Technology

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Tools to analyse cell signaling models by Collins, David Michael, 1975-

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Integrated framework of district cooling system for commercial buildings by Zamhuri, Muhammad Ikhwan

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Topics in and around higher-order Fourier analysis by Altman, D

“…</p> <p>Green and Tao’s arithmetic regularity lemma and counting lemma together apply to systems of linear forms which satisfy a particular algebraic criterion known as the ‘flag condition’. …”

Integrated framework of district cooling system for commercial buildings by Zamhuri, Muhammad Ikhwan

“…To be more holistic, a mathematical model was developed by using the general algebraic modelling system (GAMS) for optimisation of DCS to determine the minimum total energy cost, optimal capacity of DCS equipment and renewable energy (RE) and electricity consumption in order to minimise the economic and environmental effects. …”
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On &#x0393;-Interval Valued Fuzzification of Lagrange&#x2019;s Theorem of &#x0393;-Interval Valued Fuzzy Subgroups by Umer Shuaib, Abdul Razaq, Hanan Alolaiyan, Muhammad Shahram Saif, Ayesha Rafiq

“…We use this ideology to define the concepts of <inline-formula> <tex-math notation="LaTeX">$\Gamma $ </tex-math></inline-formula>-IVF cosets, <inline-formula> <tex-math notation="LaTeX">$\mathrm {\Gamma }$ </tex-math></inline-formula>-IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subgroups of <inline-formula> <tex-math notation="LaTeX">$\mathrm {\Gamma }$ </tex-math></inline-formula>-IVFSG and investigate the condition under which a <inline-formula> <tex-math notation="LaTeX">$\mathrm {\Gamma }$ </tex-math></inline-formula>-IVFS is <inline-formula> <tex-math notation="LaTeX">$\Gamma $ </tex-math></inline-formula>-IVFSG. …”
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Fully Automatic Sliding Motion Compensated and Simultaneous 4D-CBCT via Bilateral Filtering by Jun Dang, Tao You, Wenzheng Sun, Hanguan Xiao, Longhao Li, Xiaopin Chen, Chunhua Dai, Ying Li, Yanbo Song, Tao Zhang, Deyu Chen

“…PurposeTo incorporate the bilateral filtering into the Deformable Vector Field (DVF) based 4D-CBCT reconstruction for realizing a fully automatic sliding motion compensated 4D-CBCT.Materials and MethodsInitially, a motion compensated simultaneous algebraic reconstruction technique (mSART) is used to generate a high quality reference phase (e.g. 0% phase) by using all phase projections together with the initial 4D-DVFs. …”
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Potential Investigation of Linking PROSAIL with the Ross-Li BRDF Model for Vegetation Characterization by Xiaoning Zhang, Ziti Jiao, Yadong Dong, Hu Zhang, Yang Li, Dandan He, Anxin Ding, Siyang Yin, Lei Cui, Yaxuan Chang

“…Such modeled BRFs, as an essential information source, are then input into an inversion procedure that is devised through a large number of simulation analyses from some widely used physical models that can generalize such an inversion relationship between the BRFs (or their simple algebraic composite) and the biophysical/structural parameter. …”
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Properties of individual contrails: a compilation of observations and some comparisons by U. Schumann, R. Baumann, D. Baumgardner, S. T. Bedka, D. P. Duda, V. Freudenthaler, J.-F. Gayet, A. J. Heymsfield, P. Minnis, M. Quante, E. Raschke, H. Schlager, M. Vázquez-Navarro, C. Voigt, Z. Wang

“…The cross-section-integrated extinction follows an algebraic approximation. The ratio of volume to effective mean radius decreases with time. …”
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Homogeneous <italic>L_p</italic> Stability for Homogeneous Systems by Daipeng Zhang, Jaime A. Moreno, Johann Reger

“…These results are extensions to arbitrary homogeneous systems of the well-known situation for linear time-invariant systems, where the Hamilton-Jacobi inequality reduces to an algebraic Riccati inequality. A natural application of finite-gain homogeneous <inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{p}-$ </tex-math></inline-formula> stability is in the study of stability for interconnected systems. …”
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Assessment of Two Streamline Curvature Correction Methods for an Elliptic Blending Turbulence Model by Xianglong Yang, Zhenhao Liao, Lei Yang

“…One method involves modifying the dissipation term in the turbulent dissipation equation, while the other constructs a new formulation for the turbulent kinetic energy production term based on an explicit algebraic stress model. The capabilities of the proposed models are evaluated by applying them to three flows with curved surfaces; namely, the two-dimensional (2D) infinite serpentine passage flow, the 2D U-turn duct flow, and the 2D periodic hill flow. …”
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Semihypergroup-Based Graph for Modeling International Spread of COVID-<i>n</i> in Social Systems by Narjes Firouzkouhi, Reza Ameri, Abbas Amini, Hashem Bordbar

“…Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. …”
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Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement Gravity versus <i>SU</i>(∞)-QGR by Houri Ziaeepour

“…We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> group in their formulation; the necessity of a quantum time as a relational observable. …”
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An Efficient Quadrature Rule for Highly Oscillatory Integrals with Airy Function by Guidong Liu, Zhenhua Xu, Bin Li

“…The inherent high oscillation and algebraic singularity of the integrand make traditional quadrature rules impractical. …”
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Multifunctional Molecular Magnets: Magnetocaloric Effect in Octacyanometallates by Magdalena Fitta, Robert Pełka, Piotr Konieczny, Maria Bałanda

“…We present examples of magnetic entropy change &Delta;Sm and adiabatic temperature change &Delta;Tad, determined using calorimetric measurements supplemented with the algebraic extrapolation of the data down to 0 K. At the field change of 5T, the compound built of high spin clusters Ni9[W(CN)8]6 showed a maximum value of &minus;&Delta;Sm equal to 18.38 J&middot;K&minus;1 mol&minus;1 at 4.3 K, while the corresponding maximum &Delta;Tad = 4.6 K was attained at 2.2 K. …”
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Examining the Phenomenon of Porterage (Kolberi) in the City of Baneh by Akbar Zareshahabadi, Arzoo Mohmmadi

“…They believed that the borders and algebraic conditions of the region caused the city to be underdeveloped. …”
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Exploring the impacts of using Geogebra software on secondary school students’ misconceptions in trigonometric functions by F. Radmehr, H. Rahimian

“…This difficulty observed both when students calculated the periodicity from the graphs and also when calculated the periodicity from the algebraic form of trigonometric functions. The strength of using the software includes observing many trigonometric graphs in the software environment, the ability to place trigonometric functions with different input on a coordinate axis and comparing them, and the manipulations performed by the students themselves on trigonometric graphs. …”
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Optimal Integration of Dispersed Generation in Medium-Voltage Distribution Networks for Voltage Stability Enhancement by Brayan Enrique Aguirre-Angulo, Lady Carolina Giraldo-Bello, Oscar Danilo Montoya, Francisco David Moya

“…The problem is formulated through a mixed-integer nonlinear programming model (MINLP), which is solved using General Algebraic Modeling System (GAMS) software. A numerical example with a 7-bus radial distribution network is employed to introduce the usage of GAMS software to solve the proposed MINLP model. …”
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Comparison of three VST orthokeratology lenses in axial length growth and average corneal reshaping in myopia children: A retrospective self-controlled study by Anken Wang, Wansheng Zang, Li Shen, Lu Gao, Chenhao Yang

“…The average values of the above data, the average value of the decentration vector (ADV), and the average value of decentration calculated algebraically (ADA) were calculated. Results: All the three pairs (Lucid (n = 46) vs. …”
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