[4] L. Horv´ ath, K.A. Khan and J. Peˇ cari´ c, Refinements of Results about Weighted Mixed **Symmetric** **Means** and Related Cauchy **Means**, J. Inequal. Appl., Vol. 2011, Article ID 350973, 19 pages, (2011). [5] J. Jakˇ setic and J. Peˇ cari´ c, Exponential Convexity Method, Journal of Convex Analysis, to appear. [6] K. A. Khan, J. Peˇ cari´ c and I. Peri´ c, Differences of Weighted Mixed **Symmetric** **Means** and Related

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A recent refinement of the classical discrete Jensen inequality is given by Horv´ath and Peˇcari´c. In this paper, the corresponding weighted mixed **symmetric** **means** and Cauchy-type **means** are defined. We investigate the exponential convexity of some functions, study mean value theorems, and prove the monotonicity of the introduced **means**.

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Some improvements of classical Jensen’s inequality are used to define the weighted mixed **symmetric** **means**. Exponential convexity and mean value theorems are proved for the diﬀerences of these improved inequalities. Related Cauchy **means** are also defined, and their monotonicity is established as an application.

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We refer the reader to the survey article[2] and the references therein for an account of Ky Fan’s inequality. See also [11]-[16] for recent developments in this subject. Among numerous sharpenings of Ky Fan’s inequality in the literature, we note the following inequalities connecting the three classical **means**(with q i = 1/n here):

Abstract. In this paper, we extend the results in part I-III on certain inequalities involving the weighted power **means** as well as the **symmetric** **means**. These inequalities can be largely viewed as concerning the bounds for ratios of differences of **means** and can be traced back to the work of Diananda.

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As already pointed in the Introduction, the Schwab-Borchardt mean SB is of great inter- est since it includes a lot of **symmetric** **means**. Our approach includes, in turn, the mean SB. The following example explains this latter situation and that of the previous remark. It also shows that m f is not always **symmetric**.

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mean inequalities for the generalized weighted power **means** Theorem 1.1, it is natural to ask whether similar results hold for the **symmetric** **means**. Of course one may have to adjust the notion of such mixed **means** in order for this to make sense for all n. For example, when r 3, n 2, the notion of P 2,3 is not even defined. From now on, we will only focus on the extreme cases of the **symmetric** **means**; namely, r 2 or r n − 1. In these cases it is then natural to define P 1,2 x 1 , and, on recasting P n,n−1 G n/n−1 n /H n 1/n−1 , we see that it is also

Remark . The symmetry character of the above involved mean is, by deﬁnition, taken as essential hypothesis. In fact, if we attempt to extend the above concepts to non-**symmetric** **means** by keeping the same deﬁnitions (Deﬁnition . and Deﬁnition .), the simple **means** m = A / , G / , with A / (a, b) = (/)a + (/)b, G / (a, b) = a / b / , do not satisfy

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As we know, the charge distribution in – aromatic bridge (benzene ring) is **symmetric** in the plane of the molecule, **means**, the total dipole moment of benzene equals zero, adding the substituents to this ring leads to anew structure may have non – polarity and a symmetry in charge distribution (change in the polarity of the molecule).In table 7, the total dipole moment of the donor and the acceptor structures are (4.087 and 3.732) Debye, these values are independent on the number of atoms or subgroups ((substituents)) added to the original molecule but depend on the positions of these substituents in the molecule. The complex compound (D – B – A) have large value of dipole moment (19.896 Debye) corresponds to its C 1 molecular point group. This large

Why not KDM security? It might be asked why we bother to investigate soundness of coinductive methods, when there are constructions in the standard model for secure encryption under key-dependent messaging [17,19]. We note that security against adaptive corruptions is a necessary requirement for any encryption scheme used in a protocol which is run in an environment with adversarially adaptive corruptions. In such situations, once a key is corrupted, the security of the protocol will depend on the preservation of secrecy for keys which are not trivially corrupted. Even in the idealized static corruption model, a key may dynamically be revealed by the exploitation of potential weaknesses of a protocol (e.g., consider a situation where the adversary gets to alter a communicated message by replacing an “honest” key with his own key, making an honest party then encrypt a secret key under the adversarial key.) To the best of our knowledge, there are no provable constructions of KDM-secure encryption in the standard model which also provide security against adaptive corruptions. Backes et al. [8] consider a limited case in which security is defined only in a left-or-right indistinguishability sense, not addressing the above problem. In subsequent work, [6] considers the problem in its full generality as described above, but their construction is in the random-oracle model. Moreover, they do not consider the question of whether generic constructions from KDM-secure encryption schemes exist (in the standard model) which also provide security against adaptive corruptions. Related Work. Obtaining sound abstract security proofs for protocols involving **symmetric** encryption has also been considered following the ideal/real simulation paradigms of [20,47]. [7] shows that secure realization of ideal **symmetric** encryption (in the sense of reactive sim- ulatability ) is possible in their cryptographic library [9] if the commitment problem does not occur (i.e. any honest party’s key

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The existence of quasi–realistic models in which all the untwisted K¨ahler and complex structure moduli are projected out is fascinating. It offers a novel perspective on the existence of extra dimensions in string theory, and on the problem of moduli stabilization. The untwisted moduli are those that govern the underlying geometry, and hence the physics of the extra dimensions. Reparameterization invariance in string theory introduces the need for additional degrees of freedom, beyond the four space–time dimensions, to maintain the classical symmetry in the quantized theory. These additional degrees of freedom may be interpreted as extra dimensions, which are compactified and hidden from contemporary experimental observations. Thus, the consistency of string theory gives rise to the notion of extra dimensions, which in every other respect is problematic. In particular, it raises the issue of what is the mechanism that selects and fixes the parameters of the compactified space. However, if there exist string models in which all the untwisted moduli are projected out by the GSO projections, it **means** that in these vacua the parameters of the extra dimensions are frozen. In fact, in these string vacua the extra degrees of freedom needed for consistency cannot be interpreted as extra dimensions, as it is not possible to deform from their fixed values, and there is no notion of a continuous classical geometry.

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Suppose the user asks its system to use this scheme to encrypt a message M with key K and associated data A, which **means** that the system is expected to pick coins δ at random from the space D of coins for E and return ciphertext C ← E(K, M, A; δ) (where we now replace IV by δ to emphasise the fact that δ may not be surfaced). Our subverted encryption algorithm will compute C the same way, except that δ will not be chosen quite at random. Instead, it will be chosen to ensure that F ( K, C e ) = K[j] is the j-bit of the key, where F is a PRF. The subverter decryption algorithm, on receiving C, will recompute K[j] as F ( K, C). The counter e j will be maintained by the subverter algorithms in their state, so that over |K| encryptions, the entire key is leaked. The challenge here is showing that the bias created in the distribution of C is not detectable, even given the key K. Exploiting PRF security, we can move to a setting where F ( K, e ·) is replaced by a random function. Then we use an information-theoretic argument to show that the statistical distance between the real and subverted ciphertexts is small even given K. In terms of our formal definitions, big brother is undetectable.

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Despite the fact that modern aircraft are packed with sophisticated electronic equip- ment, air traffic control has always been more of an art than a science. Ground-based control essentially consists of people following the progress of aircraft represented by points (derived from radar data) on a flat display screen. The simple nature of the data available **means** that the controllers themselves are required to build and maintain a “mental picture” of extrapolated 4D traffic based on experience and other rather ill-de- fined heuristics. Having done this, the controller must mentally compare every pair of predicted trajectories to determine whether any pair of aircraft will pass within the min- imum permitted separation - in which case he is required to intervene in some way to resolve the potential conflict.

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This paper aims at filling the gaps mentioned above. 2 Specifically, I build a two-firm efficiency-wage model in which each competitor tries to overbid the wage offer of the other employer aiming at maximizing its profits. Consistently with Akerlof (1984) and Hahn (1987), I assume that for each firm the efficiency of the employed labour force is positively correlated to its own wage offer but negatively correlated to the offer put forward by the other firm. Within this framework, I discuss the shape of the strategic relation among optimal wage offers and their link with the corresponding iso-profit curves. Thereafter, considering the most recurrent adjustment mechanisms exploited in similar game-theoretic contexts (e.g. Kopel 1996 and Varian 1992), I consider the way in which the wage distribution prevailing in a **symmetric** Nash equilibrium can actually be achieved. Furthermore, taking into account possible labour market equilibria, I discuss effort cyclicality.

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of A . This **symmetric** matrix is used in statistical analysis, theory of graphs and networks[1]. Complex **symmetric** matrices arise in the study of damped vibrations of linear systems, in classical theories of wave propagation in continuous media, and in general relativity.

The fifth one deals with the hybrid BEM/FEM schemes in the time domain, which appropriately combine the advantages of both the FEM and the BEM. The finite element method, for instance, is well suited for materials with inelastic behavior. For this reason, the finite element discretization is applied to regions expected to become inelastic. On the other hand, for systems with infinite extension, which are expected to remain elastic, the use of the BEM in conjunction with the elastodynamic fundamental solution of the problem is by far more beneficial. Thus, the FEM/BEM coupling in the time domain has been successfully used to solve 2-D nonlinear dynamic soil/structure interaction problems where the inelastic structure and the surrounding soil part expected to become inelastic are simulated by the FEM and the remaining soil assumed to behave linearly by **means** of the BEM. One can mention here the works related to general 2-D structures by Pavlatos and Beskos [82] and Soares et al. [83], structures with reinforced media by Coda [84] underground structures by Adam [85] and Takemiya and Adam [86], earth dams by Abouseeda and Dakoulas [87], concrete gravity dams by Yazdchi et al. [88] and wall structures by von Estorff and Firuziaan [89].

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In Figures 9 and 10, static responses of EPRS with different thickness profiles are compared for β=0.25 and β=1.25. When the thickness variation factor is β=0.25 as seen in Figures 9-a and 10-a, the β parameter has a similar effect on displacement results for the considered thickness profiles and boundary conditions. Conversely, the static responses differ for the three different thickness profiles when the thickness variation factor is β=1.25. Displacement values of EPRS having sine variable thickness profile in Figures 9 and 10 on static responses are observed to be minimum for β=1.25. In addition, the largest displacement values occur in cosine form for β=1.25. As can be seen from Figures 7-10, the displacement values of the clamped boundary condition are always lower than the simply-supported boundary condition. As can be seen from the Figures 9 and 10, sine and cosine thickness profiles yield symmetrical displacement forms unlike the linear profile. Sine and cosine thickness profiles are **symmetric** but linear thickness profile is not **symmetric** in longitudinal direction (in ϕ direction). Therefore, the response is not **symmetric** for linear thickness profile.

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The concept of a **symmetric** bi-derivation has been introduced by Maksa in [6]. In [9], Vukman has proved some results concerning **symmetric** bi-derivation on prime and semiprime rings. Yenigul and Argac [10] studied ideals and **symmetric** bi-derivations of prime and semiprime rings. Reddy et al. [5] studied **symmetric** reverse bi-derivations on prime rings. Sapanci et al. [8] studied few results of **symmetric** bi-derivation on prime rings. In this paper, we extended some results of **symmetric** reverse bi-derivations on prime rings.

a The Au contacts in this case were measured while testing the sample and were found to have a resistance of 25 Ω (which is small compared to other samples that we tested). Both the BSTS and the Au are independent of the magnetic field and will be a constant offset to the resistance. Since Nb is a superconductor, these contacts do not have resistance. In Fig. 4.6, it can be seen that the samples have two Au contacts and two Nb contacts. This allows us to do four point measurements, which implies that we can eliminate any contributions of the cables or other parts of the setup. a Another field dependent phenomenon that we have already come across a couple of times is WAL (introduced in Section 1.3.3 and briefly discussed in Section 4.4.1). WAL is known to decrease with magnetic field, which is what we are looking for. We note that WAL can only exist in the diffusive regime and it is unclear in which regime we are. For the moment, suppose we have WAL in our system. Both the WAL and the MBS are quantum corrections to the conductance, which **means** that they are in the order of magnitude of a conductance quantum. Therefore, if the WAL correction is slightly larger than the MBS correction, it is possible that we are not able to observe the MBS at low magnetic field. However, having a look at the order of magnitude with which the conductance goes down (see Fig. 4.14b), we can immediately see that this is much larger than a conductance quantum. Therefore, even if WAL is present in this system, it cannot be responsible for a conductance decrease of this size. The possible contribution of WAL will be discussed in Section 4.5.3.

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Remark 2.7. It follows from the formal properties of Morita equivalences that a Morita equiva- lence between two algebras induces a bijection between quotients of the two algebras, in such a way that quotients corresponding to each other are again Morita equivalent. In particular, **symmetric** quotients are preserved under Morita equivalences. We describe this briefly for the convenience of the reader. Let A, B be Morita equivalent O-algebras; that is, there is an A-B -bimodule M and a B-A-bimodule N such that M , N are finitely generated projective as left and right modules, and such that we have isomorphisms of bimodules M ⊗ B N ∼ = A and N ⊗ A M ∼ = B. The functor

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