The Geometric Series Hypothesis of Leaf Area Distribution and Its Link to the Calculation of the Total Leaf Area per Shoot of <i>Sasaella kongosanensis</i> ‘Aureostriatus’ by Yong Meng, David A. Ratkowsky, Weihao Yao, Yi Heng, Peijian Shi

“…We used the formula for the sum of the first <i>j</i> terms (<i>j</i> ranging from 1 to <i>n</i>) of a geometric series (GS), with the mean of the quotients of any adjacent two terms (denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mi>q</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>A</mi></mrow></msub></mrow></semantics></math></inline-formula>) per shoot as the common ratio of the GS, to fit the cumulative leaf area observations. …”
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Extremal Results on <i>ℓ</i>-Connected Graphs or Pancyclic Graphs Based on Wiener-Type Indices by Jing Zeng, Hechao Liu, Lihua You

“…The connectivity of an incomplete graph <i>G</i>, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>κ</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula>, is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo movablelimits="true" form="prefix">min</mo><mo>{</mo><mo>|</mo><mi>W</mi><mo>|</mo><mo>|</mo><mi>W</mi><mspace width="4pt"></mspace><mi>i</mi><mi>s</mi><mspace width="4pt"></mspace><mi>a</mi><mspace width="4pt"></mspace><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>x</mi><mspace width="4pt"></mspace><mi>c</mi><mi>u</mi><mi>t</mi><mspace width="4pt"></mspace><mi>o</mi><mi>f</mi><mspace width="4pt"></mspace><mi>G</mi><mo>}</mo></mrow></semantics></math></inline-formula>. …”
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On the Normalized Laplacian Spectrum of the Zero-Divisor Graph of the Commutative Ring <inline-formula><math display="inline"><semantics><msub><mstyle mathvariant="bold"><mi mathva... by Ali Al Khabyah, Nazim, Nadeem Ur Rehman

“…The zero-divisor graph of a commutative ring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">R</mi></semantics></math></inline-formula> with a nonzero identity, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><mi mathvariant="fraktur">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>, is an undirected graph where the vertex set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><msup><mrow><mo>(</mo><mi mathvariant="fraktur">R</mi><mo>)</mo></mrow><mo>*</mo></msup></mrow></semantics></math></inline-formula> consists of all nonzero zero-divisors of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">R</mi></semantics></math></inline-formula>. …”
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The Singularity of the <i>K</i>₄ Homeomorphic Graph by Haicheng Ma

“…Insert <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>−</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>−</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>3</mn></msub><mo>−</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>4</mn></msub><mo>−</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>5</mn></msub><mo>−</mo><mn>2</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>6</mn></msub><mo>−</mo><mn>2</mn></mrow></semantics></math></inline-formula> vertices in the six edges of the complete graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>4</mn></msub></semantics></math></inline-formula>, respectively, then the resulting graph is called the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>4</mn></msub></semantics></math></inline-formula> homeomorphic graph, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>(</mo><msub><mi>a</mi><mn>1</mn></msub><mo>,</mo><msub><mi>a</mi><mn>2</mn></msub><mo>,</mo><msub><mi>a</mi><mn>3</mn></msub><mo>,</mo><msub><mi>a</mi><mn>4</mn></msub><mo>,</mo><msub><mi>a</mi><mn>5</mn></msub><mo>,</mo><msub><mi>a</mi><mn>6</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Solar-Driven Water Purification: Advancing PVA-Chitosan/PANI Hydrogel to Enhance Solar Vapor Generation for Freshwater Treatment by Flora Serati, Syazwani Mohd Zaki, Ahmad Akid Zulkifli, Siti Rabizah Makhsin

“…In this study, PVA-CS/PANi hydrogels were prepared with distinct concentrations of PVA and denoted as PVA-CS/PANi/1.3 mol.%, PVA-CS/PANi/2.7 mol.% and PVA-CS/PANi/3.9 mol.%. …”
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