scholarly journals Special value formula for the twisted triple product L-function and an application to the restricted L2-norm problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yao Cheng
Keyword(s):  
Spectral Parameter ◽  
Upper Bound ◽  
Automorphic Form ◽  
Triple Product ◽  
The Real ◽  
Central Values ◽  
Real Place ◽  
Quadratic Extensions ◽  
L2 Norm ◽  
Special Value

AbstractWe establish explicit Ichino’s formulae for the central values of the triple product L-functions with emphasis on the calculations for the real place. The key ingredient for our computations is Proposition 8 which generalizes a result in [P. Michel and A. Venkatesh, The subconvexity problem for {\rm GL}_{2}, Publ. Math. Inst. Hautes Études Sci. 111 2010, 171–271]. As an application we prove the optimal upper bound of a sum of restricted {L^{2}}-norms of the {L^{2}}-normalized newforms on certain quadratic extensions with prime level and bounded spectral parameter following the methods in [V. Blomer, On the 4-norm of an automorphic form, J. Eur. Math. Soc. (JEMS) 15 2013, 5, 1825–1852].

scholarly journals A Viable Approach to Mitigating Irreproducibility

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 205-215
Author(s):  
David Trafimow ◽  
Tonghui Wang ◽  
Cong Wang
Keyword(s):  
Upper Bound ◽  
Recent Article ◽  
Practical Problem ◽  
The Real ◽  
Viable Approach ◽  
Real Universe ◽  
The Ideal

In a recent article, Trafimow suggested the usefulness of imagining an ideal universe where the only difference between original and replication experiments is the operation of randomness. This contrasts with replication in the real universe where systematicity, as well as randomness, creates differences between original and replication experiments. Although Trafimow showed (a) that the probability of replication in the ideal universe places an upper bound on the probability of replication in the real universe, and (b) how to calculate the probability of replication in the ideal universe, the conception is afflicted with an important practical problem. Too many participants are needed to render the approach palatable to most researchers. The present aim is to address this problem. Embracing skewness is an important part of the solution.

scholarly journals Matrix Games with Interval-Valued 2-Tuple Linguistic Information

Games ◽  
2018 ◽  
Vol 9 (3) ◽  
pp. 62 ◽  
Author(s):  
Anjali Singh ◽  
Anjana Gupta
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Real World ◽  
Upper Bound ◽  
Duality Theorem ◽  
Matrix Game ◽  
Matrix Games ◽  
Linguistic Information ◽  
The Real ◽  
Interval Valued

In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.

LOWER BOUNDS FOR STREETS AND GENERALIZED STREETS

2001 ◽  
Vol 11 (04) ◽  
pp. 401-421 ◽  
Author(s):  
ALEJANDRO LÓPEZ-ORTIZ ◽  
SVEN SCHUIERER
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real Line ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Search Strategy ◽  
The Real ◽  
Simple Polygons ◽  
On Line ◽  
Special Classes

We present lower bounds for on-line searching problems in two special classes of simple polygons called streets and generalized streets. In streets we assume that the location of the target is known to the robot in advance and prove a lower bound of [Formula: see text] on the competitive ratio of any deterministic search strategy—which can be shown to be tight. For generalized streets we show that if the location of the target is not known, then there is a class of orthogonal generalized streets for which the competitive ratio of any search strategy is at least [Formula: see text] in the L2-metric—again matching the competitive ratio of the best known algorithm. We also show that if the location of the target is known, then the competitive ratio for searching in generalized streets in the L1-metric is at least 9 which is tight as well. The former result is based on a lower bound on the average competitive ratio of searching on the real line if an upper bound of D to the target is given. We show that in this case the average competitive ratio is at least 9-O(1/ log D).

Epicurus: ‘Live Hidden!’

Philosophy ◽  
1988 ◽  
Vol 63 (243) ◽  
pp. 93-104 ◽  
Author(s):  
William James Earle
Keyword(s):  
Cultural Distance ◽  
Private Life ◽  
The Real ◽  
Real Place ◽  
The World ◽  
Private And Public ◽  
Circle Of Friends ◽  
Ethics And Politics

Epicurus, though popularly and indeed nominally associated with a doctrine advocating the procurement of rather expensive pleasure, lived very simply in his garden with a circle of friends. The 14th of his Sovran Maxims or Cardinal Tenets (kuriai doxai), as collected by Diogenes Laertius, reads: ‘When tolerable security against our fellowmen is attained, then on a basis of power sufficient to afford support and of material prosperity arises in most genuine form the security of a quiet private life withdrawn from the multitude’ R. D. Hicks, the translator, gives, as an alternative to ‘power sufficient to afford support’, ‘power to expel’, but on either reading, we are to think of Epicurus's garden, both the real place and the conceptualized, or tropologized, topos of wisdom and earthly felicity, as enclosed and exclusive. This enclosure, exclusivity, and—what is also implied—abstention of its inmates from participation in the affairs of state are given apophthegmatic expression in ‘Live hidden!’ We contemplate this adage, or slogan, from an enormous cultural distance and, for most of us, ‘Live hidden!’ is much more likely to trigger secondary reflections about the relations between ethics and politics, private and public, perfection of self and improvement of the world, than it is to constitute an actual, or potential, piece of advice we might think about whether, and how, to follow.

scholarly journals WAYS OF DIMINISHING OF ERRORS OF CALCULATIONS OF COMPUTER OF AUTONOMOUS MOBILE OBJECT ARE FOR ALGORITHMS OF SLAM OF NAVIGATION

2020 ◽  
pp. 32-43
Author(s):  
Yu. A. Nitsuk ◽  
О. М. Semchak ◽  
І. V. Sharipova
Keyword(s):  
Subsequent Development ◽  
The State ◽  
Mobile Object ◽  
Frequency Filter ◽  
Mobile Unit ◽  
The Real ◽  
Real Place ◽  
The Way

A question is in-process considered, in relation to the lead through of estimation of complication of algorithms of EKF-SLAM and construction of map of locality in accordance with supporting points, from point of his algorithmically programmatic realization. It enables to determine the ways of subsequent development and adaptation of the known mathematical correlations of algorithms of EKF-SLAM and DP-SLAM for diminishing of errors of calculations of co-ordinates airborne COMPUTERS of autonomous mobile object for realization of algorithms. The estimation of the state of off-line mobile unit is arrived at by filtration of particles. The great number of hypotheses which are an eventual number is generated, which show by itself the predictable place of location of robot. Every meaningful element of map, that orienteer, in every particle can be appraised with the use of the extended filters of Kalmana, particles of robot conditioned position. And the coefficient of weight of particles settles accounts for determination of probability of hit of certain part in a final set, which will present not only the real place of location of autonomous mobile object on a map but also position of found out all orienteers. The way of modification of the known mathematical correlations of filters of Kalmana offered in-process from point of their adaptation to the features of algorithmic and programmatic realization in airborne COMPUTERS provides economy of memory of airborne COMPUTER and diminishing of necessary calculable resource It is noticed that the algorithms of realization of SLAM of navigation are changed the offered way use less of particles, than methods, based only on a frequency filter. The error of initial calculation of co-ordinates of orienteer is taken to the minimum and does not accumulate in course of time in mathematical sense.

scholarly journals ON POINT SETS IN VECTOR SPACES OVER FINITE FIELDS THAT DETERMINE ONLY ACUTE ANGLE TRIANGLES

2009 ◽  
Vol 81 (1) ◽  
pp. 114-120 ◽  
Author(s):  
IGOR E. SHPARLINSKI
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Upper Bound ◽  
Dimensional Space ◽  
Real Space ◽  
Acute Angle ◽  
Vector Spaces ◽  
Point Sets ◽  
Similar Question ◽  
The Real

AbstractFor three points$\vec {u}$,$\vec {v}$and$\vec {w}$in then-dimensional space 𝔽nqover the finite field 𝔽qofqelements we give a natural interpretation of an acute angle triangle defined by these points. We obtain an upper bound on the size of a set 𝒵 such that all triples of distinct points$\vec {u}, \vec {v}, \vec {w} \in \cZ $define acute angle triangles. A similar question in the real space ℛndates back to P. Erdős and has been studied by several authors.

scholarly journals EXACT AVERAGES OF CENTRAL VALUES OF TRIPLE PRODUCT L-FUNCTIONS

2010 ◽  
Vol 06 (07) ◽  
pp. 1609-1624 ◽  
Author(s):  
BROOKE FEIGON ◽  
DAVID WHITEHOUSE
Keyword(s):  
Triple Product ◽  
Central Values

We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla.

,,Ein Vorhof zum Paradies". Das Czernowitz-Bild in der deutsch-jüdischen Literatur

2006 ◽  
Vol 58 (3) ◽  
pp. 216-226
Author(s):  
Anna-Dorothea Ludewig
Keyword(s):  
20Th Century ◽  
19Th Century ◽  
Holocaust Survivors ◽  
The Real ◽  
Real Place ◽  
Time Period ◽  
The 19Th Century ◽  
The Relationship ◽  
The Ideal

AbstractThe present research on Czernowitz focuses mostly on the 20th century and on the works and memoirs of Holocaust survivors. But Czernowitz was at its cultural and economical height at the end of the 19th century, and it was during that time that the myth of the ,,ideal city" was established. This essay stresses the importance of that time period for understanding the ,,Czernowitz myth," and it analyzes the relationship between the ,,real" place Czernowitz and the literary topos of a ,,sunken city" (Rose Ausländer).

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