Background: A fair amount of important objects in natural images have circular and elliptical shapes. For example, the nucleus of most of the biological cells is circular, and a number of parasites such as Oxyuris have elliptical shapes in microscopic images. Hence, atomic representations by two‑ dimensional (2D) basis functions based on circle and ellipse can be useful for processing these images. The first researches have been done in this domain by introducing circlet transform. Methods: The main goal of this article is expanding the circlet to a new one with elliptical basis functions. Results: In this article, we first introduce a new transform called ellipselet and then compare it with other X‑ let transforms including 2D‑ discrete wavelet transform, dual‑ tree complex wavelet, curvelet, contourlet, steerable pyramid, and circlet transform in the application of image denoising. Conclusion: Experimental results show that for noises under 30, the ellipselet is better than other geometrical X-lets in terms of Peak Signal to Noise Ratio, especially for Lena which contains more circular structures. However, for Barbara which has fine structures in its texture, it has worse results than dual‑ tree complex wavelet and steerable pyramid.

I read with interest the article by Farzaneganet al., titled “Effects of lumbar discectomy on disability and depression in patients with chronic low back pain”. It was a very well-written article on an important subject, which has remained largely ignored. I would therefore like to congratulate the investigators for highlighting the subject. However, I have a few concerns regarding the methodology of the study. First, I am not convinced that discectomy or laminectomy is ever indicated for back pain alone. It is also unclear whether these operations can lessen chronic back pain; they could also aggravate the pain. The best surgical outcomes after discectomy or laminectomy are expected in cases of radicular leg pain that is unresponsive to the best medical management available.

In this article we investigate filters of cozero sets for real-valued continuous functions, calledcoz-filters. Much is known for z-ultrafilters and their correspondence with maximal ideals of C (X). Similarly, a correspondence will be established betweencoz-ultrafilters and minimal prime ideals of C (X). We will further notice various properties of coz-ultrafilters in relation toP-spaces and F-spaces. In the last two sections, the collection of cozultrafilters will be topologized, and then compared to the hull-kernel and the inverse topologies placed on the collection of minimal prime ideals of C (X) and general lattice-ordered groups.

In this experimental work, the polycrystalline samples of ternary compound InGaTe2 and binary compound PbT2 were initially synthesized and then by grinding and mixing given amounts of PbTe and InGaTe2 (as impurity), two types of compounds given by the formula (PbTe)1-x (InGaTe2)x having two different mole percentages of x=0.5 and x=1 were synthesized, respectively. By studying the variations of thermoelectric power (a) and electrical conductivity (er) of samples versus the temperature, the values of energy gap for the above two compounds were evaluated. Experimental results show that, the pure PbTe is a typical p type semiconductor, but introducing the ternary compound InGaTe2 into the crystal, its conductivity changes from p to n. The energy gap of PbTe is increased by increasing the mole percentage of the InGaTe2 impurity. Increasing the impurity content, up to x=0.5 mole percent causes the conductivity to increase, but further increase of the impurity content, causes the conductivity to decrease. Thermoelectric power increases with the temperature and its maximum value is larger for the compound with lesser impurity content.

In this paper we study some sufficient conditions for commutativity of a ring according to Jacobsons'idea. Jacobson proved that if R is a ring satisfying xn= x (n>1) for each x Î R, then R is commutative. In this paper, we show that R is commutative if for every x, y 2 R there exists a positive integer n= n (x, y) such that (x [x, y])n = x [x, y].