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    Magnetocaloric Effect for a <i>Q</i>-Clock-Type System by Michel Aguilera, Sergio Pino-Alarcón, Francisco J. Peña, Eugenio E. Vogel, Natalia Cortés, Patricio Vargas

    Published 2024-12-01
    “…We use lattices of different sizes with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mi>L</mi><mo>×</mo><mi>L</mi><mo>=</mo><msup><mn>8</mn><mn>2</mn></msup><mo>,</mo><msup><mn>16</mn><mn>2</mn></msup><mo>,</mo><msup><mn>32</mn><mn>2</mn></msup><mo>,</mo><msup><mn>64</mn><mn>2</mn></msup><mo>,</mo><mi>and</mi><mspace width="4pt"></mspace><msup><mn>128</mn><mn>2</mn></msup></mrow></semantics></math></inline-formula> sites, considering free boundary conditions and an external magnetic field varying between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>=</mo><mn>1.0</mn></mrow></semantics></math></inline-formula> in natural units of the system. …”
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  11. 27651

    On Discrete Shifts of Some Beurling Zeta Functions by Antanas Laurinčikas, Darius Šiaučiūnas

    Published 2024-12-01
    “…We consider the Beurling zeta function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ζ</mi><mi mathvariant="double-struck">P</mi></msub><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>=</mo><mi>σ</mi><mo>+</mo><mi>i</mi><mi>t</mi></mrow></semantics></math></inline-formula>, of the system of generalized prime numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">P</mi></semantics></math></inline-formula> with generalized integers <i>m</i> satisfying the condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>∑</mo><mrow><mi>m</mi><mo>⩽</mo><mi>x</mi></mrow></msub><mn>1</mn><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msup><mi>x</mi><mi>δ</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>⩽</mo><mi>δ</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, and suppose that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ζ</mi><mi mathvariant="double-struck">P</mi></msub><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> has a bounded mean square for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>></mo><msub><mi>σ</mi><mi mathvariant="double-struck">P</mi></msub></mrow></semantics></math></inline-formula> with some <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi mathvariant="double-struck">P</mi></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. …”
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