Faith, Understanding, Proof by A. E. Razumov

“…I believe in something and I understand something, but I do not understand everything I believe in, but sometimes I believe in something I don’t understand at all. Add the problem of proof to this. Not all that we believe in can be supported by proof. …”
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Metatranscriptomics as a tool to identify fungal species and subspecies in mixed communities – a proof of concept under laboratory conditions by Vanesa R. Marcelino, Laszlo Irinyi, John-Sebastian Eden, Wieland Meyer, Edward C. Holmes, Tania C. Sorrell

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Utilisation of an in vivo malaria model to provide functional proof for RhopH1/CLAG essentiality and conserved orthology with P. falciparum by Mitchell L. Trickey, Mrittika Chowdury, Georgina Bramwell, Natalie A. Counihan, Tania F. de Koning-Ward

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Quantum complexity phase transitions in monitored random circuits by Ryotaro Suzuki, Jonas Haferkamp, Jens Eisert, Philippe Faist

“…In our proof, we make use of percolation theory to find paths along which an exponentially long quantum computation can be run below the critical rate, and to identify events where the state complexity is reset to zero above the critical rate. …”
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A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States by Qiang Ling, Haojiang Deng

“…In the paper by Costa and Fragoso (2004), a proof was given by extending the state domain to the complex space. …”
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Short Paper - The Binary Linearization Complexity of Pseudo-Boolean Functions by Walter, Matthias

“…This motivates the definition of the linearization complexity of $f$ as the minimum such $k$. Our theoretical contributions are the proof that random polynomials almost surely have a high linearization complexity and characterizations of its value in case we do or do not restrict the set of admissible Boolean functions. …”
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A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method by Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, Mohammad W. Alomari

“…Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. …”
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Rigidity of symmetric simplicial complexes and the lower bound theorem by James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

“…The proof of our rigidity result adapts earlier ideas of Fogelsanger to the setting of symmetric simplicial complexes.…”
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Mixed Balanced Truncation for Reducing the Complexity of Large-Scale Electrical and Electronic System Simulations by Huy-Du Dao, Thanh-Tung Nguyen, Ngoc-Kien Vu, Van-Ta Hoang, Hong-Quang Nguyen

“…The main contributions of this work in developing the new reduction algorithm include the introduction of a novel definition of mixed balanced systems and theoretical advancements through the development of theorems, lemmas, and corollaries accompanied by rigorous mathematical proofs. This study makes significant theoretical contributions and provides practical solutions for designing, modeling, and reducing the complexity of electrical and electronic systems, particularly passive linear systems in general.…”
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Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations by Xinsong Yang, Shuang Ai, Tingting Su, Ancheng Chang

“…Based on Lyapunov stability theory, integral inequality Barbalat lemma, and Schur Complement lemma, rigorous proofs are given for synchronization of the complex networks. …”
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A serendipity fully discrete div-div complex on polygonal meshes by Botti, Michele, Di Pietro, Daniele A., Salah, Marwa

“…In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. …”
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A note on an application of discrete Morse theoretic techniques on the complex of disconnected graphs by Anupam Mondal, Pritam Chandra Pramanik

“…Robin Forman’s highly influential 2002 paper A User’s Guide to Discrete Morse Theory presents an overview of the subject in a very readable manner. As a proof of concept, the author determines the topology (homotopy type) of the abstract simplicial complex of disconnected graphs of order n (which was previously done by Victor Vassiliev using classical topological methods) using discrete Morse theoretic techniques, which are purely combinatorial in nature. …”
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Peculiarities of the investigation of frauds disguised as civil legal relations by K. D. Zaiats, D. D. Zaiats

“…The need to simplify the procedure of proof in proceedings on simple, minor criminal offenses related to fraud and more active use of the institution of concluding agreements provided for in Art. 468 of the CCP of Ukraine.…”
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Toward characterizing solutions to complex programming problems involving fuzzy parameters in constraints by Hamiden Khalifa, Dragan Pamučar, Seyyed Edalatpanah

“…Using the cut set concepts, the problem is converted into the complex programming. A number of basic theorems with proofs are established concerning the basic results for the fuzzy complex set of solutions for the F-CPP, and the optimality criteria of the saddle point for F-CPP with fuzzy cones is derived.…”
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The Complexity of the Minimum Sensor Cover Problem with Unit-Disk Sensing Regions over a Connected Monitored Region by Ren-Song Ko

“…This paper considers the complexity of the Minimum Unit-Disk Cover (MUDC) problem. …”
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On the Use of Molecular Weight Cutoff Cassettes to Measure Dynamic Relaxivity of Novel Gadolinium Contrast Agents: Example Using Hyaluronic Acid Polymer Complexes in Phosphate-Buff... by Nima Kasraie, Henry Wayne Oviatt, Geoffrey David Clarke

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Development of a method to achieve antegrade in situ fenestration of endovascular stent grafts in abdominal aortic aneurysms by Cyrus J. Darvish, BS, Nicholas P. Lagerman, MS, Oldrich Virag, BS, Hannah Parks, BS, Yash K. Pandya, MD, Mohammad H. Eslami, MD, David A. Vorp, PhD, Timothy K. Chung, PhD

“…This innovative approach offers a viable alternative for patients with complex AAAs.…”
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A Group Identification Protocol with Leakage Resilience of Secret Sharing Scheme by Ping Li, Shengjun Li, Hongyang Yan, Lishan Ke, Teng Huang, Alzubair Hassan

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The Impact of Uncertainty on Pedestrians’ Decision to Start Roadway Crossing during the Clearance Phase by Milan Simeunović, Andrijana Jović, Pavle Pitka, Mladen Dobrić

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Sliding-Mode Control of the Active Suspension System with the Dynamics of a Hydraulic Actuator by Rui Bai, Dong Guo

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