Atillum André, 1903 (Hymenoptera: Mutillidae) in Brazil: current and new geographic distribution records by André Luiz Marambaia, Greice Cristina Conceição da Silva, Ramon Lima Ramos, Matheus Eduardo Trindade-Santos, Roberto Alejandro Cambra, Kevin Andrew Williams

“…This contribution aims to reduce the knowledge gap on this genus, verifying the real number of species that comprise it and which actually inhabit Brazil. …”
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The 1-dimensional [lambda]-self shrinkers in R² and the nodal sets of biharmonic Steklov problems by Chang, Jui-En

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Digital Control for Dynamic Efficiency Optimization in Switching Regulators by Cheng, Lok Hin

“…The functionality of the entire system is verified with digital simulation that employs real number modeling (RNM) of the analog blocks, which enables rapid top level or functional simulation of mixed signal designs with both analog and digital blocks. …”
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U(1)-invariant special Lagrangian 3-folds I. Nonsingular solutions by Joyce, D

“…Then |z_1|^2-|z_2|^2=2a on N for some real number a. Locally, N can be written as a kind of graph of functions u,v : R^2 --> R satisfying a nonlinear Cauchy-Riemann equation depending on a, so that u+iv is like a holomorphic function of x+iy. …”

Mathematical modeling of cancer treatments with fractional derivatives: an overview by Farayola, M. F., Shafie, S., Siam, F. M., Mahmud, R., Ajadi, S. O.

“…The concept of fractional derivatives, which is still new to many mathematicians, is a generalized definition of a derivative whose order is a real number and has proved to be more effective and robust in modeling cancer treatments. …”
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Generalized Hyers–Ulam stability of ρ-functional inequalities by Sundas Nawaz, Abdul Bariq, Afshan Batool, Ali Akgül

“…Abstract In our research work generalized Hyers-Ulam stability of the following functional inequalities is analyzed by using fixed point approach: 0.1 ∥ f ( 2 x + y ) + f ( 2 x − y ) − 2 f ( x + y ) − 2 f ( x − y ) − 12 f ( x ) − ρ ( 4 f ( x + y 2 ) + 4 ( f ( x − y 2 ) − f ( x + y ) − f ( x − y ) ) − 6 f ( x ) , r ) ∥ ≥ r r + φ ( x , y ) $$\begin{aligned}& \biggl\Vert f(2x+y)+f(2x-y)-2f(x+y)-2f(x-y)-12f(x) \\& \quad {}-\rho \biggl(4f\biggl(x+\frac{y}{2}\biggr)+4\biggl(f\biggl(x- \frac{y}{2}\biggr)-f(x+y)-f(x-y)\biggr)-6f(x),r\biggr) \biggr\Vert \geq \frac{r}{r+\varphi (x, y)} \end{aligned}$$ and 0.2 ∥ f ( 2 x + y ) + f ( 2 x − y ) − 4 f ( x + y ) − 4 f ( x − y ) − 24 f ( x ) + 6 f ( y ) − ρ ( 8 f ( x + y 2 ) + 8 ( f ( x − y 2 ) − 2 f ( x + y ) − 2 f ( x − y ) ) − 12 f ( x ) + 3 f ( y ) , r ) ∥ ≥ r r + φ ( x , y ) $$\begin{aligned}& \biggl\Vert f(2x+y)+f(2x-y)-4f(x+y)-4f(x-y)-24f(x)+6f(y) \\& \qquad {}-\rho \biggl(8f\biggl(x+\frac{y}{2}\biggr)+8\biggl(f\biggl(x- \frac{y}{2}\biggr)-2f(x+y)-2f(x-y)\biggr)-12f(x)+3f(y),r\biggr) \biggr\Vert \\& \quad \geq \frac{r}{r+\varphi (x, y)} \end{aligned}$$ in the setting of fuzzy matrix, where ρ ≠ 2 $\rho \neq 2$ is a real number. We also discussed Hyers-Ulam stability from the application point of view.…”
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Bounds on the General Eccentric Connectivity Index by Xinhong Yu, Muhammad Imran, Aisha Javed, Muhammad Kamran Jamil, Xuewu Zuo

“…The general eccentric connectivity index of a graph <i>R</i> is defined as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>ξ</mi><mrow><mi>e</mi><mi>c</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>=</mo><msub><mo>∑</mo><mrow><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mi>d</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mi>e</mi><mi>c</mi><msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mi>α</mi></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is any real number, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>e</mi><mi>c</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula> represent the eccentricity and the degree of the vertex <i>u</i> in <i>R</i>, respectively. …”
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On the $ A_{\alpha^-} $-spectra of graphs and the relation between $ A_{\alpha} $- and $ A_{\alpha^-} $-spectra by Wafaa Fakieh, Zakeiah Alkhamisi, Hanaa Alashwali

“…<p>Let $ G $ be a graph with adjacency matrix $ A(G) $, and let $ D(G) $ be the diagonal matrix of the degrees of $ G $. For any real number $ \alpha\in [0, 1] $, Nikiforov defined the $ A_{\alpha} $-matrix of $ G $ as</p> <p class="disp_formula"> $ A_{\alpha}(G) = \alpha D (G) + (1 - \alpha)A (G)…”
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Iss2Image: A Novel Signal-Encoding Technique for CNN-Based Human Activity Recognition by Taeho Hur, Jaehun Bang, Thien Huynh-The, Jongwon Lee, Jee-In Kim, Sungyoung Lee

“…Iss2Image converts real number values from the <i>X</i>, <i>Y</i>, and <i>Z</i> axes into three color channels to precisely infer correlations among successive sensor signal values in three different dimensions. …”
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An Improved Approach to Direct Simulation of an Actual Almen Shot Peening Intensity Test with a Large Number of Shots by Chengyu Wang, Weigang Li, Jianjun Jiang, Xin Chao, Weikui Zeng, Jiang Xu, Jie Yang

“…The improvement of this model is mainly reflected in the large and real number of shots involved in the actual Almen intensity test, shot–shot interactions, and real-size solid finite element model of the Almen strip. …”
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Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems by Avishek Chakraborty, Sankar Prasad Mondal, Shariful Alam, Ali Ahmadian, Norazak Senu, Debashis De, Soheil Salahshour

“…In this platform, we also created the perception of de-bipolarization for a triangular bipolar rneutrosophic number with the help of well-known techniques so that any bipolar neutrosophic fuzzy number of any type can be smoothly converted into a real number instantly. Creating a problem using bipolar neutrosophic perception is a more reliable, accurate, and trustworthy method than others. …”
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Banach Fixed Point Theorem in Extended <i>b</i>_v(<i>s</i>)-Metric Spaces by Anil Kumar

“…We define the class of extended <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>b</mi><mi>v</mi></msub><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>-metric spaces by replacing the real number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>≥</mo><mn>1</mn></mrow></semantics></math></inline-formula> with a strictly increasing continuous function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> in the definition of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>b</mi><mi>v</mi></msub><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>-metric space. …”
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Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions by Sondekola Rudra Swamy, Basem Aref Frasin, Ibtisam Aldawish

“…For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> a real number, Fekete–Szegö functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>−</mo><mi>δ</mi><msubsup><mi>d</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></msubsup><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for functions in the special family is also estimated. …”
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Mitigating Computer Limitations in Replicating Numerical Simulations of a Neural Network Model With Hodgkin-Huxley-Type Neurons by Paulo H. Lopes, Paulo H. Lopes, Bruno Cruz Oliveira, Anderson Abner de S. Souza, Wilfredo Blanco, Wilfredo Blanco

“…After all, the research community must be aware that conducting analyses with numerical simulations that use real number operations can lead to different conclusions.…”
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Parametrization and Optimal Tuning of Constrained Series PIDA Controller for IPDT Models by Mikulas Huba, Pavol Bistak, Damir Vrancic

“…Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. …”
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Adherence to interferon β treatment in Kosovan multiple sclerosis registry by Blerim Myftiu, Edmond Komoni, Edita Malazogu, Fisnik Jashari, Shpresa Beqiri Rashiti, Melihate Pushka, Adnan Biqku, Syzana Aliçkaj Prebreza, Valbona Rrahmani Spanca, Jehona Rrustemi Bytyqi, Nexhmedin Shala, Afrim Blyta

“…The number of missed doses was calculated as a difference between the number of doses a patient had to withdraw from the treatment start to the cut-off date and the real number of doses taken from the MS unit. Missed doses were compared to gender, age, time since the diagnosis, time from the diagnosis to the treatment start, clinical type of MS, expanded disability status scale (EDSS), and duration of the treatment. …”
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Pareto-optimal data compression for binary classification tasks by Tegmark, Max Erik, Wu, Tailin

“…We first show how a random variable X (an image, say) drawn from a class Y∈{1,…,n} can be distilled into a vector W=f(X)∈Rn−1 losslessly, so that I(W,Y)=I(X,Y) ; for example, for a binary classification task of cats and dogs, each image X is mapped into a single real number W retaining all information that helps distinguish cats from dogs. …”
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Pareto-Optimal Data Compression for Binary Classification Tasks by Tegmark, Max Erik, Wu, Tailin

“…We first show how a random variableX(an image, say) drawnfrom a classY∈ {1, ...,n}can be distilled into a vectorW=f(X)∈Rn−1losslessly, so thatI(W,Y) =I(X,Y); for example, for a binary classification task of cats and dogs, each imageXis mapped into a single real numberWretaining all information that helps distinguish cats fromdogs. …”
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Neuro-RAM unit with applications to similarity testing and compression in spiking neural networks by Lynch, Nancy, Parter, Merav, Musco, Cameron

“…It also establishes a separation between feedforward networks whose gates spike with sigmoidal probabilities, and well-studied deterministic sigmoidal networks, whose gates output real number sigmoidal values, and which can implement a neuro-RAM much more efficiently.…”
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Optimal Algebraic Manipulation Detection Codes in the Constant-Error Model by Padró, Carles, Xing, Chaoping, Cramer, Ronald

“…In all our results, the error probability ϵ can be chosen as an arbitrarily small positive real number.…”
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