scholarly journals Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative IsP-Convex

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
A. Barani ◽  
S. Barani ◽  
S. S. Dragomir
Keyword(s):  
Second Derivative ◽  
Absolute Value ◽  
Right Hand ◽  
Special Means ◽  
Second Derivatives ◽  
The Absolute ◽  
The Right

We extend some estimates of the right-hand side of Hermite-Hadamard-type inequalities for functions whose second derivatives absolute values areP-convex. Applications to some special means are considered.

scholarly journals HERMITE–HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE FIRST DERIVATIVE IS P-CONVEX

2011 ◽  
Vol 86 (1) ◽  
pp. 126-134 ◽  
Author(s):  
A. BARANI ◽  
S. BARANI
Keyword(s):  
Type Inequality ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
First Derivative ◽  
Right Hand ◽  
Special Means ◽  
The Absolute ◽  
The Right

AbstractIn this paper we extend some estimates of the right-hand side of a Hermite–Hadamard type inequality for functions whose derivatives’ absolute values are P-convex. Applications to the trapezoidal formula and special means are introduced.

scholarly journals New inequalities of Hermite-Hadamard type for n-times differentiable convex and concave functions with applications

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2609-2621
Author(s):  
M.A. Latif ◽  
S.S. Dragomir
Keyword(s):  
Concave Functions ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Special Cases ◽  
New Inequalities

In this paper, a new identity for n-times differntiable functions is established and by using the obtained identity, some new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex and concave functions. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are convex and concave functions as special cases. Our results may provide refinements of some results already exist in literature. Applications to trapezoidal formula and special means of established results are given.

scholarly journals Some (p,q)-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 683 ◽  
Author(s):  
Humaira Kalsoom ◽  
Muhammad Amer ◽  
Moin-ud-Din Junjua ◽  
Sabir Hussain ◽  
Gullnaz Shahzadi
Keyword(s):  
Convex Functions ◽  
Integral Type ◽  
Partial Derivatives ◽  
Functions Of Two Variables ◽  
Right Hand ◽  
The Absolute ◽  
The Right ◽  
Quasi Convexity

In this paper, we present the preliminaries of ( p , q ) -calculus for functions of two variables. Furthermore, we prove some new Hermite-Hadamard integral-type inequalities for convex functions on coordinates over [ a , b ] × [ c , d ] by using the ( p , q ) -calculus of the functions of two variables. Furthermore, we establish an identity for the right-hand side of the Hermite-Hadamard-type inequalities on coordinates that is proven by using the ( p , q ) -calculus of the functions of two variables. Finally, we use the new identity to prove some trapezoidal-type inequalities with the assumptions of convexity and quasi-convexity on coordinates of the absolute values of the partial derivatives defined in the ( p , q ) -calculus of the functions of two variables.

scholarly journals Synchronization Error of Drum Kit Playing with a Metronome at Different Tempi by Professional Drummers

2011 ◽  
Vol 28 (5) ◽  
pp. 491-503 ◽  
Author(s):  
Shinya Fujii ◽  
Masaya Hirashima ◽  
Kazutoshi Kudo ◽  
Tatsuyuki Ohtsuki ◽  
Yoshihiko Nakamura ◽  
...  
Keyword(s):  
Time Series ◽  
The Other ◽  
Synchronization Error ◽  
Left Hand ◽  
Snare Drum ◽  
Right Hand ◽  
The Absolute ◽  
The Right

the present study examined the synchronization error (SE) of drum kit playing by professional drummers with an auditory metronome, focusing on the effects of motor effectors and tempi. Fifteen professional drummers attempted to synchronize a basic drumming pattern with a metronome as precisely as possible at tempi of 60, 120, and 200 beats per minute (bpm). In the 60 and 120 bpm conditions, the right hand (high-hat cymbals) showed small mean SE (∼2 ms), whereas the left hand (snare drum) and right foot (bass drum) preceded the metronome by about 10 ms. In the 200 bpm condition, the right hand was delayed by about 10 ms relative to the metronome, whereas the left hand and right foot showed small SE (∼1 ms). The absolute values of SE were smaller than those reported in previous tapping studies. In addition, the time series of SE were significantly correlated across the motor effectors, suggesting that each limb synchronized in relation to the other limbs rather than independently with the metronome.

Über die Vierfingerfurche und ihre Übergangsformen, insbesondere bei Zwillingen

1954 ◽  
Vol 3 (1) ◽  
pp. 50-83 ◽  
Author(s):  
Irmgard Tillner
Keyword(s):  
Left Hand ◽  
Female Sex ◽  
Right Hand ◽  
Average Population ◽  
Transitional Forms ◽  
Male Sex ◽  
The Absolute ◽  
Hereditary Character ◽  
The Right

SUMMARYWe researched a total number of 3974 persons for the frequency of simian lines and all the material is based on 375 monozygotic, 360 dizygotic, 226 twins of different sex and 2045 single persons of two groups of the population. We classified the material collected into three degrees of impress of the simian line: a little form « 3 », a middle form « 2 » and the classical simian line, called form « 1 ». The form « 3 », which was more frequent to be seen than the form « 1 » and « 2 » seems to contain characteristics of « accidental » genesis without any relation to classical simian lines. That was to be found especially in the case that the little form was only on the surface of one hand. In contrast to that the form on both hands allows the deduction, that there must exist a relation to simian lines. The relations between the forms « 1 » and « 2 » are more evident than these of the little form « 3 ».The classical simian line seems to be more frequent on the left hand and with the male sex than on the right hand and with the female sex. This picture is a counterpart to the behaviour of thenar patterns.The result of the average population ist applicable to twins, too. Furthermore it was possible to show by arithmetic, that the concordant reactions of the monozygotics and the discordant reactions of the dizygotics are based on the hereditary character of simian lines and their transitional forms. There is a remarcable difference between monozygotic and dizygotic which is caused by the fact, that discordance of monozygotic is to be found in the case that one partner is one-sided affected with. Moreover the discordant forms become less frequent, if the degree of impress increases. The dizygotics are in the inverse ratio.The absolute concordance, too, that means the same degree of impress on the same hands of both partners, is more frequently to be found in the case of monozygotic than in the case of dizygotic.

On: “Maximum uncertainty of interval velocity estimates” by Z. Hajnal and I. T. Serada (GEOPHYSICS, 46, November 1981, 1543‐1547).

Geophysics ◽  
1985 ◽  
Vol 50 (11) ◽  
pp. 1790-1790
Author(s):  
I. Késmárky
Keyword(s):  
Statistical Analysis ◽  
Practical Result ◽  
Interval Velocity ◽  
Right Hand ◽  
The Absolute ◽  
The Right

In these remarks I draw attention to some practical aspects of the paper by Hajnal and Serada. Although conclusions drawn from equation (27) are clear and concise, the statistical analysis of equation (26) would lead to a more practical result. Taking the absolute values of all the terms on the right‐hand side of equation (26) may lead to a pessimistic overestimate of [Formula: see text].

scholarly journals New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

2016 ◽  
Vol 2 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Samet Erden ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Green Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Convex Mappings ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Type Integral

Abstract We derive some Hermite Hamamard type integral inequalities for functions whose second derivatives absolute value are convex. Some eror estimates for the trapezoidal formula are obtained. Finally, some natural applications to special means of real numbers are given

Dynamics of reflex cocontraction in hermit crab abdomen: experiments and a systems model

1993 ◽  
Vol 69 (6) ◽  
pp. 1904-1917 ◽  
Author(s):  
W. D. Chapple
Keyword(s):  
Hermit Crab ◽  
Muscle Activation ◽  
Muscle Stiffness ◽  
Second Derivative ◽  
Pass Filter ◽  
Absolute Value ◽  
First Derivative ◽  
Systems Model ◽  
Fourth Segment ◽  
The Absolute

1. Both stretch and release of the ventral superficial muscles (VSM) in the abdomen of the hermit crab, Pagurus pollicarus, activate the VSM motoneurons in the intact animal and in the isolated abdomen. 2. This reflex was studied by recording intracellularly from muscle fibers innervated by single motoneurons during stretch and release of the VSM. The three motoneurons of the right fourth segment respond to both stretch and release with a phasic burst lasting approximately 250 ms. The burst in the two tonic motoneurons has two components, a short burst lasting 10-20 ms, with a latency from the beginning of stretch of 60-90 ms, and a longer burst of variable length, with a latency of 120 ms. Ramp stretches of different amplitudes and velocities were used to show that the first component is proportional to the absolute value of the second derivative of force and the second component to the absolute value of the first derivative of force. 3. Stretch and release of the VSM also simultaneously evoke phasic bursts in the motoneurons of the dorsal superficial muscles and the VSM circular muscles (functional antagonists of the longitudinal VSM), as well as in contralateral homologues of the same segment and in ipsilateral homologues of the next anterior segment. The effect of this coactivation is to stiffen the abdomen in response to perturbations in any direction. 4. Stretch or release of phasic mechanoreceptors in the VSM evokes this reflex. Isometric electrical stimulation of the isolated muscle also activates them, showing that they are transducing changes in force and suggesting that they operate to increase muscle stiffness by positive feedback. 5. A mathematical systems model of this reflex, composed of two parallel pathways activating the motoneurons, was constructed. The first pathway produces a signal proportional to the absolute value of the second derivative of force, the second pathway a signal proportional to the first derivative of force. The sum of the signals from the two pathways is filtered by an adaptation process, which is followed by a low-pass filter representing muscle activation kinetics. The muscle activation signal is then fed back to multiple muscle force. 6. Simulations using this model generate the phasic bursts to stretch and release as well as reproducing the frequency dependence of this reflex. The predominant action of this reflex is to enhance muscle stiffness.

scholarly journals Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups: Erratum

2015 ◽  
Vol 25 (3) ◽  
pp. 484-485 ◽  
Author(s):  
TIM AUSTIN
Keyword(s):  
First Line ◽  
Absolute Value ◽  
Formula Group ◽  
The Absolute ◽  
Image Position ◽  
The Right ◽  
Random Groups ◽  
Complex Valued

In my recent paper [1] there is a mistake in the proof of Corollary 3. The first line of the displayed equation in that proof asserts that \[\int_G|\langle u,\pi^g v\rangle_V|^2\,\rm{d} g = \int_G\langle u\otimes u,(\pi^g\otimes \pi^g)(v\otimes v)\rangle_{V\otimes V}\, \rm{d} g.\] However, since the paper uses complex-valued representations, the integrand on the right here may not retain the absolute value of that on the left. Without this equality, the proof of Corollary 3 can no longer be reduced to an application of Lemma 2. However, it can be proved directly from Schur Orthogonality along very similar lines to the proof of Lemma 2.

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