A syntactic realization theorem for justification logics

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms \$mathsfd\$, \$mathsft\$, \$mathsfb\$, \$mathsf4\$, and \$mathsf5\$ with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting's realization merging technique. We further strengthen the realization theorem for \$mathsfKB5\$ and \$mathsfS5\$ by showing that the positive introspection operator is superfluous.

Intraoperative Patient-Specific Reconstruction of Partial Bone Flap Defects After Convexity Meningioma Resection

OBJECTIVE: To evaluate implant accuracy and cosmetic outcome of a new intraoperative patient-specific cranioplasty method after convexity meningioma resection. METHODS: The patient's own bone flap served as a template to mold a negative form with the use of polymethyl methacrylate (PMMA). The area of bone invasion was determined and broadly excised under white light illumination with a safety margin of at least 1 cm. The definitive replica was cast within the remaining bone flap frame and the imprint. Clinical and radiologic follow-up examinations were performed 3 months after surgery. RESULTS: Four women and two men (mean age 51.4 years ± 12.8) underwent reconstruction of bone flap defects after meningioma resection. Mean duration of intraoperative reconstruction of the partial bone flap defects was 19 minutes ± 4 (range 14-24 minutes). Implant sizes ranged from 17-35 cm(2) (mean size 22 cm(2) ± 8). Radiologic and clinical follow-up examinations revealed excellent implant alignment and favorable cosmesis (visual analogue scale for cosmesis [VASC] = 97 ± 5) in all patients. CONCLUSIONS: Patient-specific reconstruction of partial bone flap defects after convexity meningioma resection using the presented intraoperative PMMA cast method resulted in excellent bony alignment and a favorable cosmetic outcome. Relatively low costs and minimized operation time for adjustment and insertion of the cranioplasty implant justify use of this method in small bony defects as well.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.