Optimal Pebbling in Products of Graphs

We prove a generalization of Graham's Conjecture for optimal pebbling with arbitrary sets of target distributions. We provide bounds on optimal pebbling numbers of products of complete graphs and explicitly find optimal $t$-pebbling numbers for specific such products. We obtain bounds on optimal pebbling numbers of powers of the cycle $C_5$. Finally, we present explicit distributions which provide asymptotic bounds on optimal pebbling numbers of hypercubes.Comment: 28 pages, 1 figur

Awareness and attitudes amongst basic surgical trainees regarding radiation in orthopaedic trauma surgery

This study investigated the awareness and attitudes of basic surgical trainees. Trainees were asked to answer questions from a pre-set questionnaire. Fifty basic surgical trainees from England and Wales were involved in the study. The areas covered were basic knowledge of radiation hazards, use of protective wear, pregnancy test in female trauma victims of reproductive age, and principles of safe radiation. All the questions were asked in the context of orthopaedic trauma surgery. All questions were evidence based

A preliminary study of the effect of closed incision management with negative pressure wound therapy over high-risk incisions

Background Certain postoperative wounds are recognised to be associated with more complications than others and may be termed high-risk. Wound healing can be particularly challenging following high-energy trauma where wound necrosis and infection rates are high. Surgical incision for joint arthrodesis can also be considered high-risk as it requires extensive and invasive surgery and postoperative distal limb swelling and wound dehiscence are common. Recent human literature has investigated the use of negative pressure wound therapy (NPWT) over high-risk closed surgical incisions and beneficial effects have been noted including decreased drainage, decreased dehiscence and decreased infection rates. In a randomised, controlled study twenty cases undergoing distal limb high-energy fracture stabilisation or arthrodesis were randomised to NPWT or control groups. All cases had a modified Robert-Jones dressing applied for 72 h postoperatively and NPWT was applied for 24 h in the NPWT group. Morphometric assessment of limb circumference was performed at six sites preoperatively, 24 and 72 h postoperatively. Wound discharge was assessed at 24 and 72 h. Postoperative analgesia protocol was standardised and a Glasgow Composite Measure Pain Score (GCPS) carried out at 24, 48 and 72 h. Complications were noted and differences between groups were assessed. Results Percentage change in limb circumference between preoperative and 24 and 72 h postoperative measurements was significantly less at all sites for the NPWT group with exception of the joint proximal to the surgical site and the centre of the operated bone at 72 h. Median discharge score was lower in the NPWT group than the control group at 24 h. No significant differences in GCPS or complication rates were noted. Conclusions Digital swelling and wound discharge were reduced when NPWT was employed for closed incision management. Larger studies are required to evaluate whether this will result in reduced discomfort and complication rates postoperatively

Male antene: postupci smanjivanja izmjera i primjene

The paper presents research results in the field of small antennas obtained at the Department of Wireless Communications, Faculty of Electrical Engineering and Computing, University of Zagreb. A study comparing the application of several miniaturization techniques on a shorted patch antenna is presented. Single and dual band shorted patch antennas with notches and/or slot are introduced. A PIFA designed for application in mobile GSM terminals is described. The application of stacked shorted patches as array elements for a mobile communication base station as well as for electromagnetic field sensor is presented. The design of single and dual band folded monopoles is described. Prototypes of the presented antennas have been manufactured and their characteristics were verified by measurements.U radu su prikazani rezultati istraživanja u području malih antena ostvareni na Zavodu za Radiokomunikacije, Sveučilišta u Zagrebu Fakulteta elektrotehnike i računarstva. Prikazana je primjena više postupaka za smanjivanje izmjera skraćene mikrotrakaste antene. Opisane su izvedbe skraćenih mikrotrakastih antena s urezima i prorezom za rad u jednom i u dva frekvencijska područja. Prikazana je izvedba planarne invertirane F-antene (PIFA) za primjenu u ručnim terminalima sustava pokretnih komunikacija GSM. Višeslojne skraćene mikrotrakaste antene uporabljene su za izvedbu antenskog niza za baznu postaju sustava pokretnih komunikacija te kao elementi osjetila za mjerenje jakosti elektromagnetskog polja. Prikazana je izvedba savijenih monopolnih antena za rad u jednom te u dva frekvencijska pojasa. Izrađeni su prototipovi opisanih antena i mjerenjima su ispitane njihove osobine

Average and worst case number of nodes in decision diagrams of symmetric multiple-valued functions

IEEE Transactions on Computers, Vol. 46, No.4, pp. 491-494, April 1997.This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted

Diameter bounds, fractional . . .

We give upper bounds on t-pebbling numbers of graphs of small diameter and investigate the relationships between these results and those relating to fractional pebbling. Furthermore, we present a connection between optimal pebbling and linear optimization and utilize this relationship in analyzing various graphs. We introduce the optimal fractional pebbling number of a graph and provide a combinatorial interpretation. Finally, we explore a generalization of graph pebbling by allowing the target to be any distribution of a given size