Detecting self-similarity in surface microstructures

The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend on the kind of the carpet. These peaks point to the presence of self-similarity even for randomly perturbed initial fractal sets. This is also demonstrated for the model population of particles diffusing over the surface considered by Van Siclen, Phys. Rev. E 56 (1997) 5211. These results allow the subtle self-similarity traces to be explored.Comment: 9 pages, 4 figures, presented at ECOSS18 (Vienna) Sept. 199

Preference programming and inconsistent interval matrices

The problem of derivation of the weights of altematives from pairwise comparison matrices is long standing. In this paper,Lexicographic Goal Programming (LGP) has been used to find out weights from pairwise inconsistent interval judgment matrices. A number of properties and advantages of LGP as a weight determination technique have been explored. An algorithm for identification and modification of inconsistent bounds is also provided. The proposed technique has been illustrated by means of numerical examples.Analytic hierarchy process; Interval judgment; Preferente programming

Kirillov-Reshetikhin crystals B^{7,s} for type E_7^1

We construct a combinatorial crystal structure on the Kirillov-Reshetikhin crystal B^{7,s} in type E_7^1, where 7 is the unique node in the orbit of 0 in the affine Dynkin diagram

Macdonald Polynomials and level two Demazure modules for affine sln+1\mathfrak{sl}_{n+1}

We define a family of symmetric polynomials $G_{\nu,\lambda}(z_1,\cdots, z_{n+1},q)$ indexed by a pair of dominant integral weights. The polynomial $G_{\nu,0}(z,q)$ is the specialized Macdonald polynomial and we prove that $G_{0,\lambda}(z,q)$ is the graded character of a level two Demazure module associated to the affine Lie algebra $\widehat{\mathfrak{sl}}_{n+1}$. Under suitable conditions on $(\nu,\lambda)$ (which includes the case when $\nu=0$ or $\lambda=0$) we prove that $G_{\nu,\lambda}(z,q)$ is Schur positive and give explicit formulae for them in terms of Macdonald polynomials

Outcome Analysis of Intra-Articular Scapula Fracture Fixation with Distal Radius Plate: A Multicenter Prospective Study

Background: Scapula fractures occur in approximately 1% of all fractures and constitute about 3% - 5% of all injuries of the shoulder joint. Objectives: This study aimed to evaluate the clinical outcomes of 20 surgically treated patients with displaced glenoid fractures after stabilization with distal radius plate. Methods: Between 2012 and 2015, at 2 centers (HMCH & SHCE) of Bhubaneswar Odisha, we stabilized 20 scapular intra-articular fractures surgically with distal radius locking plate and studied the outcome of the surgeries. The outcome of the 20 fractures was determined using the Constant and Murley score. Both shoulders were assessed and the score on the injured side was given as a percentage of that on the uninjured side. Results: The median score was 88% (mean 65%, range 30 to 100). The median score for strength was 21/25 (mean 19, range 0 to 25) and that for pain 11/15 (mean 11, range 5 to 15). The median functional score was 16/20 (mean 15, range 0 to 20). The mean range of active abduction of the shoulder was 135° (20 to 180), the mean range of flexion 138° (20 to 180) and the mean range of external rotation 38° (0 to 100). Five patients showed excellent result; 11 patients showed good result; three patients showed fair result and one patient had poor outcome according to the Constant-Murley score. A superficial infection settled with antibiotics after operation in one patient whose score at final follow-up was 96%. In one patient, delayed healing was reported because of infection. One patient with stiffness of the shoulder at six weeks underwent manipulation under anesthesia with a follow-up score of 81%. Conclusions: Various fixation modalities have been described in the literature, however fixation of intra-articular fracture of glenoid with distal radius locking plate for articular reconstruction in the presented series provides good functional outcome with early restoration of the range of motion of the shoulder