Exterior square gamma factors for cuspidal representations of GLn: finite field analogs and level-zero representations

AbstractFor a p-adic local field F of characteristic 0, with residue field {\mathfrak{f}}, we prove that the Rankin–Selberg gamma factor of a pair of level zero representations of linear general groups over F is equal to a gamma factor of a pair of corresponding cuspidal representations of linear general groups over {\mathfrak{f}}. Our results can be used to prove a variant of Jacquet’s conjecture on the local converse theorem.

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Exterior square gamma factors for cuspidal representations of $$\mathrm {GL}_n$$: simple supercuspidal representations

The Ramanujan Journal ◽

10.1007/s11139-021-00476-x ◽

2021 ◽

Author(s):

Rongqing Ye ◽

Elad Zelingher

Keyword(s):

Supercuspidal Representations ◽

Exterior Square ◽

Cuspidal Representations

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A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

Methods of Information in Medicine ◽

10.1055/s-0038-1636689 ◽

1987 ◽

Vol 26 (03) ◽

pp. 117-123

Author(s):

P. Tautu ◽

G. Wagner

Keyword(s):

Stochastic Model ◽

Gaussian Process ◽

Covariance Function ◽

Neoplastic Disease ◽

Disease Phenotype ◽

Probabilistic Representation ◽

Temporal Behaviour ◽

Continuous Trait ◽

Continuous Parameter ◽

Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

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Beta dynamical systems over the formal fields

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.51.2014.4.1291 ◽

2014 ◽

Vol 51 (4) ◽

pp. 454-465

Author(s):

Lu-Ming Shen ◽

Huiping Jing

Keyword(s):

Dynamical Systems ◽

Finite Field ◽

Haar Measure ◽

Laurent Series ◽

Formal Laurent Series ◽

Almost All

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q ((X^{ - 1} ))$$ \end{document} denote the formal field of all formal Laurent series x = Σ n=ν∞anX−n in an indeterminate X, with coefficients an lying in a given finite field \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}. For any \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} with deg β > 1, it is known that for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} (with respect to the Haar measure), x is β-normal. In this paper, we show the inverse direction, i.e., for any x, for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document}, x is β-normal.

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ANALISIS TATANIAGA TANDAN BUAH SEGAR KELAPA SAWIT DI DESA TEMPAKAN KECAMATAN BATU ENGAU KABUPATEN PASER (Marketing Analysis of Fresh Fruit Bunches of Oil Palm in Tempakan Village, Batu Engau Subregency, Paser Regency)

JURNAL AGRIBISNIS DAN KOMUNIKASI PERTANIAN (Journal of Agribusiness and Agricultural Communication) ◽

10.35941/jakp.2.2.2019.2686.113-120 ◽

2019 ◽

Vol 2 (2) ◽

pp. 113

Author(s):

SIMON SUTRADO SIMANJUNTAK ◽

ACHMAD ZAINI

Keyword(s):

Oil Palm ◽

Sampling Method ◽

Marketing Channel ◽

Marketing Channels ◽

Fresh Fruit ◽

Snowball Sampling ◽

Level Zero ◽

Average Share ◽

Marketing Analysis ◽

Fresh Fruit Bunches

The purposes of this study were to know marketing channel, marketing margin, share, and marketing profit of fresh fruit bunches of oil palm in Tempakan Village, Batu Engau Subregency, Paser Regency. The study was conducted from June to August 2016. The sampling method was done with two ways as random sampling in farmer level and in marketing channel as snowball sampling. Data analysis were done by calculating marketing margin, share, and marketing profit. The results of this study showed that there are two marketing channels in reserach location are channel of level zero and channel of level one. Marketing margin in farmer level was Rp40.39 kg-1 and margin in whole trader level was Rp314.44 kg-1. The average share of farmer level was 97.58% and in trader level was 81.48%. Margin and share that profitable for farmer is at channel of level zero. The average of profit in whole trader level of fresh fruit bunches was 112.75%, that meant marketing by whole trader is profitable.

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Valued Field Graph and Some Related Parameters

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.30 ◽

2020 ◽

pp. 389-395

Author(s):

G. Suresh Singh ◽

P. K. Prasobha

Keyword(s):

Finite Field ◽

Independence Number ◽

Valued Field ◽

Vertex Set ◽

Adic Valuation

Let $K$ be any finite field. For any prime $p$, the $p$-adic valuation map is given by $\psi_{p}:K/\{0\} \to \R^+\bigcup\{0\}$ is given by $\psi_{p}(r) = n$ where $r = p^n \frac{a}{b}$, where $p,a,b$ are relatively prime. The field $K$ together with a valuation is called valued field. Also, any field $K$ has the trivial valuation determined by $\psi{(K)} = \{0,1\}$. Through out the paper K represents $\Z_q$. In this paper, we construct the graph corresponding to the valuation map called the valued field graph, denoted by $VFG_{p}(\Z_{q})$ whose vertex set is $\{v_0,v_1,v_2,\ldots, v_{q-1}\}$ where two vertices $v_i$ and $v_j$ are adjacent if $\psi_{p}(i) = j$ or $\psi_{p}(j) = i$. Here, we tried to characterize the valued field graph in $\Z_q$. Also we analyse various graph theoretical parameters such as diameter, independence number etc.

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