scholarly journals Trans-Dichotomous Algorithms without Multiplication —some Upper and Lower Bounds

1997 ◽  
Vol 4 (12) ◽  
Author(s):  
Andrej Brodnik ◽  
Peter Bro Miltersen ◽  
J. Ian Munro
Keyword(s):  
Linear Space ◽  
Lower Bounds ◽  
Query Time ◽  
Upper And Lower Bounds ◽  
Boolean Operations ◽  
And Shifts ◽  
Necessary And Sufficient ◽  
The Way

We show that on a RAM with addition, subtraction, bitwise<br />Boolean operations and shifts, but no multiplication, there is a<br />trans-dichotomous solution to the static dictionary problem using<br />linear space and with query time sqrt(log n(log log n)^(1+o(1))). On<br />the way, we show that two w-bit words can be multiplied in<br />time (log w)^(1+o(1)) and that time Omega(log w) is necessary, and that<br />Theta(log log w) time is necessary and sufficient for identifying the<br />least significant set bit of a word.

Capacity Estimates for Planar Cantor-Like Sets

1974 ◽  
Vol 26 (5) ◽  
pp. 1169-1172
Author(s):  
Carl David Minda
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Elementary Approach ◽  
Principal Tool ◽  
Linear Problems ◽  
Necessary And Sufficient ◽  
Positive Capacity ◽  
Capacity Estimates

Upper and lower bounds for the capacity of planar Cantor-like sets are presented. Chebichev polynomials are the principal tool employed in the derivation of these estimates. A necessary and sufficient condition for certain planar Cantor-like sets to have positive capacity is obtained. Related one-sided capacitary estimates for more general Cantor-like sets can be found in [3, pp. 106-109]. Techniques analogous to those used in this paper yield similar results for linear Cantor-like sets which are well-known [2, pp. 150-161]. The use of Chebichev polynomials to obtain these results provides an alternate, possibly more elementary, approach to these linear problems.

Three-terminal communication channels

1971 ◽  
Vol 3 (1) ◽  
pp. 120-154 ◽  
Author(s):  
Edward C. Van Der Meulen
Keyword(s):  
Mutual Information ◽  
Lower Bounds ◽  
Communication Channel ◽  
Communication Channels ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Symmetric Structure ◽  
Necessary And Sufficient ◽  
Positive Capacity

The problem of transmitting information in a specified direction over a communication channel with three terminals is considered. Examples are given of the various ways of sending information. Basic inequalities for average mutual information rates are obtained. A coding theorem and weak converse are proved and a necessary and sufficient condition for a positive capacity is derived. Upper and lower bounds on the capacity are obtained, which coincide for channels with symmetric structure.

Three-terminal communication channels

1971 ◽  
Vol 3 (01) ◽  
pp. 120-154 ◽  
Author(s):  
Edward C. Van Der Meulen
Keyword(s):  
Mutual Information ◽  
Lower Bounds ◽  
Communication Channel ◽  
Communication Channels ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Symmetric Structure ◽  
Necessary And Sufficient ◽  
Positive Capacity

The problem of transmitting information in a specified direction over a communication channel with three terminals is considered. Examples are given of the various ways of sending information. Basic inequalities for average mutual information rates are obtained. A coding theorem and weak converse are proved and a necessary and sufficient condition for a positive capacity is derived. Upper and lower bounds on the capacity are obtained, which coincide for channels with symmetric structure.

scholarly journals Finite automata with undirected state graphs

2021 ◽  
Author(s):  
Martin Kutrib ◽  
Andreas Malcher ◽  
Christian Schneider
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Deterministic Case ◽  
Boolean Operations ◽  
State Complexity ◽  
Descriptional Complexity ◽  
Language Classes ◽  
Different Types ◽  
State Graphs

AbstractWe investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then, the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.

scholarly journals Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Zhen-Hang Yang ◽  
Ying-Qing Song ◽  
Yu-Ming Chu
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Power Mean ◽  
Seiffert Mean ◽  
Second Seiffert Mean ◽  
Necessary And Sufficient ◽  
The Second Seiffert Mean

We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean.

SOME GAP THEOREMS FOR GRADIENT RICCI SOLITONS

2012 ◽  
Vol 23 (07) ◽  
pp. 1250072 ◽  
Author(s):  
MANUEL FERNÁNDEZ-LÓPEZ ◽  
EDUARDO GARCÍA-RÍO
Keyword(s):  
Lower Bounds ◽  
Ricci Tensor ◽  
Sufficient Conditions ◽  
Ricci Soliton ◽  
Upper And Lower Bounds ◽  
Ricci Solitons ◽  
Gradient Ricci Soliton ◽  
Gradient Ricci Solitons ◽  
Necessary And Sufficient ◽  
Gap Theorems

Necessary and sufficient conditions for a gradient Ricci soliton to be Einstein are given, showing that they can be expressed in terms of upper and lower bounds on the behavior of the Ricci tensor when evaluated on the gradient of the potential function of the soliton.

Praxeology, Imperatives, and Shifts of View

2018 ◽  
Author(s):  
Benj Hellie
Keyword(s):  
Practical Reason ◽  
First Person ◽  
Third Person ◽  
And Shifts ◽  
Practical Metaphysics ◽  
The Way

Recent neo-Anscombean work in praxeology (aka ‘philosophy of practical reason’), salutarily, shifts focus from an alienated ‘third-person’ viewpoint on practical reason to an embedded ‘first-person’ view: for example, the ‘naive rationalizations’ of Michael Thompson, of form ‘I am A-ing because I am B-ing’, take up the agent’s view, in the thick of action. Less salutary, in its premature abandonment of the first-person view, is an interpretation of these naive rationalizations as asserting explanatory links between facts about organically structured agentive processes in progress, followed closely by an inflationary project in ‘practical metaphysics’. If, instead, praxeologists chase first-personalism all the way down, both fact and explanation vanish (and with them, the possibility of metaphysics): what is characteristically practical is endorsement of nonpropositional imperatival content, chained together not explanatorily, but through limits on intelligibility. A connection to agentive behavior must somehow be reestablished—but this can (and can only) be done ‘transcendentally’.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

Sign in / Sign up

Export Citation Format

Share Document