Vertebral Column Resection for Rigid Spinal Deformity

Study Design: Broad narrative review. Objective: To review the evolution, operative technique, outcomes, and complications associated with posterior vertebral column resection. Methods: A literature review of posterior vertebral column resection was performed. The authors’ surgical technique is outlined in detail. The authors’ experience and the literature regarding vertebral column resection are discussed at length. Results: Treatment of severe, rigid coronal and/or sagittal malalignment with posterior vertebral column resection results in approximately 50–70% correction depending on the type of deformity. Surgical site infection rates range from 2.9% to 9.7%. Transient and permanent neurologic injury rates range from 0% to 13.8% and 0% to 6.3%, respectively. Although there are significant variations in EBL throughout the literature, it can be minimized by utilizing tranexamic acid intraoperatively. Conclusion: The ability to correct a rigid deformity in the spine relies on osteotomies. Each osteotomy is associated with a particular magnitude of correction at a single level. Posterior vertebral column resection is the most powerful posterior osteotomy method providing a successful correction of fixed complex deformities. Despite meticulous surgical technique and precision, this robust osteotomy technique can be associated with significant morbidity even in the most experienced hands.

Additive ρ-functional inequalities in β-homogeneous normed spaces

In this paper, we solve the following additive ?-functional inequalities ||f (x + y) - f (x) - f (y)|| ? ???(2f (x+y/2) - f(x) + -f (y))??, (1) where ? is a fixed complex number with |?|<1, and ??2f(x+y/2)-f(x)- f(y)???||?(f(x+y)-f(x)-f(y))||, (2) where ? is a fixed complex number with |?|<1/2 , and prove the Hyers-Ulam stability of the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive ?-functional equations associated with the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces.

Common reducing unitary subspaces and decoherence in quantum systems

Maps of the form Phi(X) =sum_{i=1}^s A_iXA^*, where A_1, . . . ,A_s are fixed complex n by n matrices and X is any complex n by n matrix are used in quantum information theory as representations of quantum channels. This article deals with computable conditions for the existence of decoherence--free subspaces for Phi. Since the definition of decoherence-free subspace for quantum channels relies only on the matrices A1, . . . ,As, the term of common reducing unitary subspace is used instead of the original one. Among the main results of the paper, there are computable conditions for the existence of common eigenvectors. These are related to common reducing unitary subspaces of dimension one. The new results on common eigenvectors provide new effective condition for the existence of common invariant subspaces of arbitrary dimensions.

ZEROS OF THE ESTERMANN ZETA FUNCTION

In this paper we investigate the zeros of the Estermann zeta function $E(s; k/ \ell , \alpha )= { \mathop{\sum }\nolimits}_{n= 1}^{\infty } {\sigma }_{\alpha } (n) \exp (2\pi ink/ \ell ){n}^{- s} $ as a function of a complex variable $s$, where $k$ and $\ell $ are coprime integers and ${\sigma }_{\alpha } (n)= {\mathop{\sum }\nolimits}_{d\vert n} {d}^{\alpha } $ is the generalized divisor function with a fixed complex number $\alpha $. In particular, we study the question on how the zeros of $E(s; k/ \ell , \alpha )$ depend on the parameters $k/ \ell $ and $\alpha $. It turns out that for some zeros there is a continuous dependency whereas for other zeros there is not.

Bilaterally Symmetrical Multiple Impacted Permanent Teeth in a Nonsyndromic Patient: A Rare Finding

ABSTRACT While impaction of tooth is widespread and common, multiple impacted teeth by itself is a rare condition which often is found in association with syndromes and also rarely reported in the literature. In some cases, however, impaction of multiple teeth is not accompanied by a fixed complex of symptoms. A 51- year-old male reported to our clinic with pain and sensitivity of his maxillary right last molar and mandibular anteriors respectively. IOPA and panoramic views revealed 4 impacted teeth in mandible (bilateral cuspids and I bicuspids) and 6 impacted teeth in maxilla (bilateral cuspids, I and II bicuspids). A total of 10 permanent teeth were impacted. In our case medical and family history along with extraoral examination were not suggestive of any syndrome or metabolic disorder. The rareness is the bilateral symmetrical pattern of impaction. How to cite this article Joyce S, Mathias V, Rao BHS. Bilaterally Symmetrical Multiple Impacted Permanent Teeth in a Nonsyndromic Patient: A Rare Finding. World J Dent 2013;4(1):72-73.

Linear Independence of -Logarithms over the Eisenstein Integers

For fixed complex with , the -logarithm is the meromorphic continuation of the series , into the whole complex plane. If is an algebraic number field, one may ask if are linearly independent over for satisfying . In 2004, Tachiya showed that this is true in the Subcase , , , and the present authors extended this result to arbitrary integer from an imaginary quadratic number field , and provided a quantitative version. In this paper, the earlier method, in particular its arithmetical part, is further developed to answer the above question in the affirmative if is the Eisenstein number field , an integer from , and a primitive third root of unity. Under these conditions, the linear independence holds also for , and both results are quantitative.