Edge Roman domination on graphs

An edge Roman dominating function of a graph $G$ is a function $f\colon E(G) \rightarrow \{0,1,2\}$ satisfying the condition that every edge $e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e')=2$. The edge Roman domination number of $G$, denoted by $\gamma'_R(G)$, is the minimum weight $w(f) = \sum_{e\in E(G)} f(e)$ of an edge Roman dominating function $f$ of $G$. This paper disproves a conjecture of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad stating that if $G$ is a graph of maximum degree $\Delta$ on $n$ vertices, then $\gamma_R'(G) \le \lceil \frac{\Delta}{\Delta+1} n \rceil$. While the counterexamples having the edge Roman domination numbers $\frac{2\Delta-2}{2\Delta-1} n$, we prove that $\frac{2\Delta-2}{2\Delta-1} n + \frac{2}{2\Delta-1}$ is an upper bound for connected graphs. Furthermore, we provide an upper bound for the edge Roman domination number of $k$-degenerate graphs, which generalizes results of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad. We also prove a sharp upper bound for subcubic graphs. In addition, we prove that the edge Roman domination numbers of planar graphs on $n$ vertices is at most $\frac{6}{7}n$, which confirms a conjecture of Akbari and Qajar. We also show an upper bound for graphs of girth at least five that is 2-cell embeddable in surfaces of small genus. Finally, we prove an upper bound for graphs that do not contain $K_{2,3}$ as a subdivision, which generalizes a result of Akbari and Qajar on outerplanar graphs

THE ACUTE EFFECT OF UPPER EXTREMITY PLYOMETRIC TRAINING

The purpose of this study was to probe the acute effect of the performance of upper extremity muscle groups after the plyometric training intervention. The participants were 13 healthy male college students. The force transducers (300kg, 200 Hz) and EMG sensor (1000 Hz) were taken to diagnose the acute effects of strength and muscle activation done by upper extremity pre and post plyometric training (load :24kg, 12 repetiiion times Iset, 3 set), and pair t-test was taken to test the significance(a=.05). The result showed that the strength after the upper extremity plyometric training intervention obviously had decreased 8% (

A Simple Model for Cavity Enhanced Slow Lights in Vertical Cavity Surface Emission Lasers

We develop a simple model for the slow lights in Vertical Cavity Surface Emission Lasers (VCSELs), with the combination of cavity and population pulsation effects. The dependences of probe signal power, injection bias current and wavelength detuning for the group delays are demonstrated numerically and experimentally. Up to 65 ps group delays and up to 10 GHz modulation frequency can be achieved in the room temperature at the wavelength of 1.3 $\mu$m. The most significant feature of our VCSEL device is that the length of active region is only several $\mu$m long. Based on the experimental parameters of quantum dot VCSEL structures, we show that the resonance effect of laser cavity plays a significant role to enhance the group delays

Rdzeniowy zespół twarzowo-palcowy: częsty zespół w nietypowej lokalizacji

Background and purpose Cheiro-oral syndrome (COS) is an established neurological entity characterized by a sensory impairment confined to the mouth angle and ipsilateral finger(s)/ hand. The current understanding of localization is a concomitant involvement of the spinothalamic and trigeminothalamic tract between the cortex and pons. The cervical spinal cord has not been mentioned in this situation yet, and this unusual location may heretofore increase the risk of misdiagnosis. Material and methods Six patients who presented with unilateral COS due to cervical cord disorder are reported. Results All patients were women and their age ranged between 42 and 70 years. Their neurological deficits included unilateral paraesthesiae restricted to cheiro-oral distribution, positive radicular sign, and mild change of tendon reflex. Cervical spinal stenosis at middle/lower cervical spine with variable magnitude of cord compression and intrinsic cord damage was found. A diagnostic dilemma obviously arises from the lack of tangible neurological signs or typical pattern of myelopathy, in addition to the previous concept of cerebral involvement. A benign course ensued in all reported patients. Conclusions Cheiro-oral syndrome can be an early neurological sign for cervical cord disorder; it further suggests that it is a strong neurological but weak localizing sign. A reciprocal influence of multiple factors is considered to generate COS at the cervical cord. Therefore, an absence of brain pathology should lead to a thorough examination of the cervical cord in case of COS.Wstęp i cel pracy Zespół twarzowo-palcowy (ZTP) jest znanym zespołem neurologicznym, który cechuje się niedoczulicą ograniczoną do kącika ust i palców ręki lub ręki po tej samej stronie. Bieżący stan wiedzy dotyczący lokalizacji uszkodzenia w tym zespole wskazuje na jednoczesne zajęcie dróg rdzeniowo-wzgórzowej i trójdzielno-wzgórzowej pomiędzy mostem i korą mózgową. W tym kontekście nie wymieniano dotąd uszkodzenia rdzenia kręgowego w odcinku szyjnym, a taka nietypowa lokalizacja uszkodzenia może zwiększyć ryzyko błędnego rozpoznania miejsca uszkodzenia. Materiał i metody W pracy przedstawiono dane dotyczące 6 pacjentek z jednostronnym ZTP spowodowanym występowaniem nieprawidłowości w obrębie rdzenia kręgowego. Wyniki Zakres wieku pacjentek wynosił od 42 do 70 lat. Objawy neurologiczne obejmowały jednostronne parestezje ograniczone do obszaru twarzy i ręki, objaw korzeniowy i niewielkie nieprawidłowości w zakresie odruchów głębokich. Stwierdzono występowanie zwężenia kanału kręgowego w środkowej lub dolnej części odcinka szyjnego z uciskiem rdzenia kręgowego i uszkodzeniem wewnątrz rdzenia kręgowego. Wątpliwości diagnostyczne wynikały z braku typowych objawów neurologicznych mielopatii i stwierdzenia lokalizacji zmian nieodpowiadającej wcześniejszym opiniom na temat mózgowego pochodzenia zespołu. U wszystkich opisywanych pacjentek przebieg schorzenia był łagodny. Wnioski Zespół twarzowo-palcowy może być wczesnym objawem neurologicznym nieprawidłowości w obrębie rdzenia kręgowego. Stanowi istotny objaw neurologiczny, ale jego wartość lokalizacyjna jest niewielka. Powstawanie ZTP wskutek uszkodzenia rdzenia kręgowego wynika z wzajemnych oddziaływań wielu czynników. W razie braku uchwytnej patologii mózgu należy w przypadkach ZTP przeprowadzić szczegółowe badania rdzenia kręgowego w odcinku szyjnym

The Liquid Sensor Using Thin Film Bulk Acoustic Resonator with C-Axis Tilted AlN Films

Dual-mode thin film bulk acoustic resonator (TFBAR) devices are fabricated with c-axis tilted AlN films. To fabricate dual-mode TFBAR devices, the off-axis RF magnetron sputtering method for the growth of tilted piezoelectric AlN thin films is adopted. In this report, the AlN thin films are deposited with tilting angles of 15° and 23°. The frequency response of the TFBAR device with 23° tilted AlN thin film is measured to reveal its ability to provide dual-mode resonance. The sensitivities of the longitudinal and shear modes to mass loading are calculated to be 2295 Hz cm2/ng and 1363 Hz cm2/ng with the mechanical quality factors of 480 and 287, respectively. The sensitivities of the longitudinal and shear modes are calculated to be 0 and 15 Hz cm2/μg for liquid loading