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    On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) by E. M. E. Zayed, M. A. El-Moneam

    Published 2007-01-01
    “…,x−1,x0 are arbitrary positive real numbers, while k is a positive integer number.…”
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    Effect of Metadoxine on Chronic Primary Hepatopathies in Canines:  Number of Cases by Paula María Bermúdez-Duarte, José Alfredo Rivera-Rojas

    Published 2023-09-01
    “…A decrease in the occurrence of vomiting and anorexia was observed (p=0.03), a non-significant increase in ALT and ALP (p=0.84; p=0.43), a reduction in bile acids (p=0.4), and no change in ultrasound score (p=0.42) or histopathological diagnosis (p>0.05). …”
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  9. 169

    Covariance of the number of real zeros of a random trigonometric polynomial by K. Farahmand, M. Sambandham

    Published 2006-01-01
    “…For random coefficients aj and bj we consider a random trigonometric polynomial defined as Tn(θ)=∑j=0n{ajcos⁡jθ+bjsin⁡jθ}. The expected number of real zeros of Tn(θ) in the interval (0,2π) can be easily obtained. …”
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  10. 170

    Effect of Atomic Number on Plasma Pinch Properties and Radiative Emissions by Walid Sahyouni, Alaa Nassif

    Published 2021-01-01
    “…Simulation was performed with Lee’s code on an NX2 dense plasma focus at a constant gas pressure value (P0=0.5 torr). The results showed that the minimum radius of the plasma focus in the case of the hydrogen plasma pinch was 0.30 cm and in the case of the argon plasma pinch 0.17 cm, and this affected the value of the radiation emission as it was 7.8×10−6 J and 11 J for the hydrogen and argon pinch, respectively. …”
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    Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order by Takao Komatsu, B. Sury

    Published 2025-01-01
    “…We study the formulas for binomial sums of harmonic numbers of higher order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover></mstyle><msubsup><mi>H</mi><mi>k</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msubsup><mfenced separators="" open="(" close=")"><mstyle scriptlevel="0" displaystyle="true"><mfrac linethickness="0pt"><mi>n</mi><mi>k</mi></mfrac></mstyle></mfenced><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>q</mi><mo>)</mo></mrow><mi>k</mi></msup><msup><mi>q</mi><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msup><mo>=</mo><msubsup><mi>H</mi><mi>n</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msubsup><mo>−</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover></mstyle><msub><mi mathvariant="script">D</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><msup><mi>q</mi><mi>j</mi></msup><mi>j</mi></mfrac></mstyle><mspace width="0.166667em"></mspace><mo>.…”
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    Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers by Awad A. Bakery, Afaf R. Abou Elmatty

    Published 2020-01-01
    “…We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s−numbers is simple Banach space.…”
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