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    Analytic Aspects of the Generalized Second-Order Central Trinomial Coefficients by Yu-Yang Zhang, Hao Pan, Lei Chen

    Published 2025-04-01
    “…We show that all zeros of the polynomial <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><msup><mi mathvariant="script">T</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msup></mrow><mi>n</mi></msub><mrow><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>⌊</mo><mrow><mi>n</mi><mo>/</mo><mn>2</mn></mrow><mo>⌋</mo></mrow></msubsup><mrow><msup><mi>T</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow><msup><mi>x</mi><mi>k</mi></msup></mrow></mrow></semantics></math></inline-formula> are real. …”
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    On Signifiable Computability: Part II: An Axiomatization of Signifiable Computation and Debugger Theorems by Vladimir A. Kulyukin

    Published 2025-03-01
    “…The first theorem shows that, for a singifiably partially computable function signified by a program on a finite-memory device <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula>, the memory capacity of <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula> is exceeded when running the program on signifiable discretely finite real numbers outside of the function’s domain. …”
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