existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations in connection with the maximizing problem for the functional r u u lq u lp in w01 p 0 we consider the equation div u p 2 u x u q 2 u x x 1 p resp q p e has no nontrivial resp nonnegative nontrivial solution belonging to the class p u w01 p lq xi u q 2u lp p 1 i 1 2 n w01 p provided that is star shaped the crucial point of the proof of our result is to obtain an l estimate of weak solutions and to verify a certain pohozaev type inequality for weak solutions belonging to p

positive solutions for a class of equations with a p laplace like operator and weights abstract in this paper we will study the problem of existence of positive solutions to the problem d a r u b r g u 0 a e in 0 r lim r 0 a r u r 0 u r 0 where is an odd increasing homeomorphism of r and g c r is such that g z 0 for all z 0 with g 0 0 the functions a and b that we will refer to as weight functions satisfy a r 0 b r 0 for all r 0 r and are such that a b c 1 0 r l 1 0 r if has the form z z m z and a r r n 1 a r b r r n 1 b r n 2 then solutions of problem d provide solutions with radial symmetry for the problem p div a x m u u b x g u 0 x u 0 x where b 0 r denotes the ball with center 0 and radius r 0 in r n

perturbation of the tangential slit by conformal maps abstract for a tangential slit the behavior of the driving function in the loewner differential equation is less clear in this paper we investigate the tangential slit where is a univalent real analytic function near the origin and where is a circular arc tangent at the origin our main aim is to give an interesting way to prove the asymptotic property of the driving function which generates the tangential slit

communication over mimo x channels interference alignment decomposition and performance analysis in a multiple antenna system with two transmitters and two receivers a scenario of data communication known as the x channel is studied in which each receiver receives data from both transmitters in this scenario it is assumed that each transmitter is unaware of the other transmitter s data noncooperative scenario this system can be considered as a combination of two broadcast channels from the transmitters points of view and two multiple access channels from the receivers points of view taking advantage of both perspectives two signaling schemes for such a scenario are developed in these schemes some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple antenna broadcast subchannels or two noninterfering multiple antenna multiple access subchannels the main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain mg it is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable mg in particular it is shown that in some specific cases the achieved mg is the same as the mg of the system if full cooperation is provided either between the transmitters or between the receivers in the second part of the paper it is shown that by using mixed design schemes rather than decomposition schemes and taking the statistical properties of the interference terms into account the power offset of the system can be improved the power offset represents the horizontal shift in the curve of the sum rate versus the total power in decibels

on feasibility of interference alignment in mimo interference networks we explore the feasibility of interference alignment in signal vector space based only on beamforming for k user mimo interference channels our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry it is well known e g from bezout s theorem that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables following this intuition we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables rigorous connections between feasible and proper systems are made through bernshtein s theorem for the case where each transmitter uses only one beamforming vector the multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems in this case we show that the connection between feasible and proper systems can be further strengthened since the equivalency between feasible and proper systems does not always hold by including standard information theoretic outer bounds in the feasibility analysis

on the existence of sle trace finite energy drivers and non constant kappa existence of loewner trace is revisited we identify finite energy paths the skeleton of wiener measure as natural class of regular drivers for which we find simple and natural estimates in terms of their cameron martin norm secondly now dealing with potentially rough drivers a representation of the derivative of the inverse of the loewner flow is given in terms of a rough and then pathwise follmer integral assuming the driver within a class of ito processes an exponential martingale argument implies existence of trace in contrast to classical exact sle computations our arguments are well adapted to perturbations such as non constant kappa assuming 2 for technical reasons and additional finite energy drift terms

generalized compute compress and forward compute and forward cf harnesses interference in wireless communications by exploiting structured coding the key idea of cf is to compute integer combinations of code words from multiple source nodes rather than to decode individual code words by treating others as noise compute compress and forward ccf can further enhance the network performance by introducing compression operations at receivers in this paper we develop a more general compression framework termed generalized ccf gccf where the compression function involves the selection of message segments over finite fields we show that gccf achieves a broader compression rate region than ccf we also compare our compression rate region with the fundamental slepian wolf sw region we show that gccf is optimal in the sense of achieving the minimum total compression rate we also establish the criteria under which gccf achieves the sw region in addition we consider a two hop relay network employing the gccf scheme we formulate a sum rate maximization problem and develop an approximate algorithm to solve the problem numerical results are presented to demonstrate the performance superiority of gccf over ccf and other schemes

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

infinitely many radially symmetric solutions for a quasilinear elliptic problem in a ball the authors improve the results of struwe under the hypothesis that f ismerely a locally lipschitz function they are able to deal with cases wherethe growth of f exceeds the sobolev limit exponent in fact their resultssuggest that it is sufficient to have the growth conditions only for u 0 orfor u 0 oru 0 0 our aim here is to extend the results of castro and kurepa to theproblem e

the covariant measure of sle on the boundary we construct a natural measure supported on the intersection of a chordal sle curve with mathbb r in the range 4 8 the measure is a function of the sle path in question assuming that boundary measures transform in a d dimensional way where d is the hausdorff dimension of gamma cap mathbb r we show that the measure we construct is up to multiplicative constant the unique measure valued function of the sle path that satisfies the domain markov property

a dimension spectrum for sle boundary collisions we consider chordal sle curves for where the intersection of the curve with the boundary is a random fractal of almost sure hausdorff dimension we study the random sets of points at which the c

compute and forward harnessing interference through structured codes interference is usually viewed as an obstacle to communication in wireless networks this paper proposes a new strategy compute and forward that exploits interference to obtain significantly higher rates between users in a network the key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise after decoding these linear equations the relays simply send them towards the destinations which given enough equations can recover their desired messages the underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field this scheme is applicable even if the transmitters lack channel state information

existence and uniqueness for a class of quasilinear elliptic boundary value problems abstract we prove existence and uniqueness of positive solutions for the boundary value problem r n 1 u r n 1 f u u 0 u 1 0 where x x p 2x f x xp 1 may not be decreasing on 0 and is a large parameter

a signal space aligned network coding approach to distributed mimo this paper studies an uplink distributed mimo dmimo system that consists of k users and k prime distributed base stations bss where the bss are connected to a central unit cu via independent rate constrained backhaul bh links we propose a new signal space aligned network coding scheme first a network coding generator matrix is selected subject to certain structural properties next distributed linear precoding is employed by the users to create aligned signal spaces at the bss according to the pattern determined by the network coding generator matrix for each aligned signal space at a bs physical layer network coding is utilized to compute the corresponding network coded nc messages where the actual number of nc messages forwarded to the cu is determined by the bh rate constraint we derive an achievable rate of the proposed scheme based on the existence of the nc generator matrix and signal space alignment precoding matrices for dmimo with two and three bss the achievable rates and degrees of freedom dof are evaluated and shown to outperform existing schemes for example for dmimo with two bss where each user and bs have n and n prime antennas respectively the proposed scheme achieves a dof of 2 min left n n prime right 1 if the bh capacity scales like left 2 min left n n prime right 1 right log snr this leads to greater dof compared to that utilizes the strategy for interference channel whose dof is min left n n prime right numerical results demonstrate the performance advantage of the proposed scheme

on sufficient conditions for the existence of radially symmetric solutions of the p laplace equation abstract we consider the dirichlet problem for the p laplace equation with a nonlinear source new a priori estimates for solutions are established in particular we obtain an explicit formula which shows the dependence of the existence of a weak bounded radially symmetric solution on the dimension of the problem

on the existence of sign changing bound state solutions of a quasilinear equation abstract in this paper we establish the existence of bound state solutions having a prescribed number of sign changes for p m u f u 0 x r n n m 1 where m u u m 2 u our result is new even for the case of the laplacian m 2

on a class of semilinear elliptic systems abstract this paper deals with the existence of positive solutions to a dirichlet problem for the superlinear elliptic system u f v v g u on a ball where is a positive parameter and f 0 g 0 may be negative

infinitely many radial solutions for a p laplacian problem p superlinear at the origin abstract we prove the existence of infinitely many radial solutions for a p laplacian dirichlet problem which is p superlinear at the origin the main tool that we use is the shooting method we extend for more general nonlinearities the results of j iaia in j iaia radial solutions to a p laplacian dirichlet problem appl anal 58 1995 335 350 previous developments require a behavior of the nonlinearity at zero and infinity while our main result only needs a condition of the nonlinearity at zero

positive radial solutions for dirichlet problems with mean curvature operators in minkowski space abstract in this paper by using leray schauder degree arguments and critical point theory for convex lower semicontinuous perturbations of c 1 functionals we obtain existence of classical positive radial solutions for dirichlet problems of type div v 1 v 2 f x v 0 in b r v 0 on b r here b r x r n x r and f 0 r 0 r is a continuous function which is positive on 0 r 0

collisions and spirals of loewner traces we analyze loewner traces driven by functions asymptotic to 1 t we prove a stability result when 6 4 and show that 4 can lead to non locally connected hulls as a consequence we obtain a driving term t so that the hulls driven by t are generated by a continuous curve for all 0 with 6 4 but not when 4 so that the space of driving terms with continuous traces is not convex as a byproduct we obtain an explicit construction of the traces driven by 1 t and a conceptual proof of the corresponding results of kager nienhuis and kadanoff

schramm s formula and the green s function for multiple sle we construct martingale observables for systems of multiple sle curves by applying screening techniques within the cft framework recently developed by kang and makarov extended to admit multiple sles we illustrate this approach by rigorously establishing explicit expressions for the green s function and schramm s formula in the case of two curves growing towards infinity in the special case when the curves are fused and start at the same point some of the formulas we prove were predicted in the physics literature

existence and uniqueness of fast decay entire solutions of quasilinear elliptic equations we prove the existence and uniqueness of fast decay solutions and clarify the structure of positive radial solutions of the quasilinear elliptic equation mu f u 0 in rn where m denotes the m laplace operator and f has a supercritical growth for small u 0 and a subcritical growth for large u our proofs use only elementary arguments based on several variational identities and a maximum principle of peletier and serrin