Differential forms and k-Minkowski spacetime from extended twist

We analyze bicovariant differential calculus on $\kappa$-Minkowski spacetime. It is shown that corresponding Lorentz generators and noncommutative coordinates compatible with bicovariant calculus cannot be realized in terms of commutative coordinates and momenta. Furthermore, $\kappa$-Minkowski space and NC forms are constructed by twist related to a bicrossproduct basis. It is pointed out that the consistency condition is not satisfied. We present the construction of $\kappa$-deformed coordinates and forms (super-Heisenberg algebra) using extended twist. It is compatible with bicovariant differential calculus with $\kappa$-deformed $\mathfrak{igl}(4)$-Hopf algebra. The extended twist leading to $\kappa$-Poincar\'{e}-Hopf algebra is also discussed.Comment: 15 pages, minor typos corrected to match the published versio

Utjecaj terapije kontinuiranim pozitivnim tlakom u dišnim putevima na kognitivne evocirane potencijale P300

Obstructive sleep apnea (OSA) is a sleep-related breathing disorder characterized by obstructions of the upper airway during sleep, resulting in repetitive breathing pauses accompanied by oxygen desaturation and arousal from sleep. OSA can be successfully treated with continuous positive airway pressure (CPAP), weight loss, positional therapy, oral appliances, hypoglossal nerve stimulation, and surgical procedures. It has been observed that untreated OSA is related to chronic disorders including hypertension, arrhythmias, congestive heart failure, coronary heart disease, diabetes mellitus, hyperlipidemia, stroke, depression, and cognitive decline. Event-related potentials (ERPs) is the procedure that has been widely used for evaluating cognitive brain functions. Using auditory event-related potentials (P300), this study aimed to examine the effect of CPAP therapy on cognitive functions in patients with moderate and severe OSA. The results of the study showed improvement in P300 latency and amplitude after 3 months of CPAP therapy, indicating a positive effect of CPAP therapy in the prevention of cognitive decline in patients with OSA.Opstruktivna apneja u spavanju (OSA) je poremećaj disanja u spavanju karakteriziran opstrukcijom gornjih dišnih puteva tijekom spavanja koji dovodi do prestanka disanja u spavanju, desaturacije krvi kisikom i buđenja. OSA se uspješno liječi uređajima za potpomognuto disanje s neprekinutim pozitivnim tlakom (CPAP), gubitkom tjelesne težine, pozicijskom terapijom, oralnim udlagama, stimulacijom živca hipoglosusa i operativnim liječenjem. Opaženo je da je neliječena OSA povezana s kroničnim poremećajima, uključujući arterijsku hiperteziju, aritmije, kongestivno zatajenje srca, koronarnu srčanu bolest, šećernu bolest, hiperlipidemiju, moždani udar, depresiju i kognitivno propadanje. Kognitivni evocirani potencijali se koriste za proučavanje kognitivnih funkcija. Cilj ovog rada je ispitati učinak terapije CPAP-om na kognitivne funkcije bolesnika s umjerenom i teškom OSA-om koristeći slušne kognitivne evocirane potencijale. Rezultati ove studije su pokazali poboljšanje P300 latencija i amplituda, ukazujući na pozitivni učinak terapije CPAP – om u prevenciji kognitivnog poremećaja u bolesnika s OSA-om

Učinak antiepileptika na kognitivne evocirane potencijale P300 u bolesnika s epilepsijom

Epilepsy is one of the most prevalent chronic neurological diseases, affecting about 70 million people worldwide. Patients with epilepsy often encounter cognitive dysfunction, which is influenced by different factors including age at the onset of epilepsy, etiology of epilepsy, type of seizures, seizure frequency and duration, psychiatric comorbidity, and antiepileptic drug (AED) therapy. Event-related potentials are useful, noninvasive, objective clinical and research instrument for evaluation of cognitive functions in patients. The aim of this study was to investigate and determine the effect of AED monotherapy and polytherapy on cognitive changes in patients with epilepsy, detected with P300 event-related potentials and compared with age- and gender-matched healthy individuals. The study was conducted in 82 patients with generalized and focal epilepsy and 82 healthy individuals aged 18-65 years. Cognitive evoked P300 potentials were recorded in all study subjects using auditory ‘oddball’ paradigm. The results showed the patients taking AED polytherapy to have a significantly longer P300 latency and significantly lower N200-P300 amplitude. These results indicate that AED polytherapy might worsen cognitive impairment in patients with epilepsy.Epilepsija je jedna od najčešćih kroničnih neuroloških bolesti od koje boluje oko 70 milijuna ljudi diljem svijeta. Bolesnici s epilepsijom često imaju poremećaj kognitivnih funkcija uzrokovan početkom bolesti, vrstom epileptičkih napadaja, trajanjem bolesti i antiepileptičkim lijekovima. Kognitivni evocirani potencijali P300 su korisna, neinvazivna, objektivna klinička i istraživačka metoda za ispitivanje kognitivnih funkcija. Cilj ovoga istraživanja bio je ispitati i utvrditi učinak antiepileptičkih lijekova (AEL) u monoterapiji i politerapiji na kognitivne promjene u bolesnika s epilepsijom uz pomoć kognitivnih evociranih potencijala P300 i usporediti ih sa zdravim pojedincima usklađenim prema dobi i spolu. U ispitivanju je sudjelovalo 82 bolesnika s generaliziranom i žarišnom epilepsijom i 82 zdrava pojedinca u dobi od 18-65 godina. Kognitivni evocirani potencijali P300 su snimani koristeći slušnu oddball paradigmu. Rezultati ove studije ukazuju na to da bolesnici na politerapiji AEL imaju značajno produženu latenciju vala P300 i značajno nižu amplitudu N200-P300. Prema rezultatima ove studije može se zaključiti kako politerapija AEL u bolesnika s epilepsijom može dovesti do pogoršanja kognitivnog poremećaja

kappa-Deformed Phase Space, Hopf Algebroid and Twisting

Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for κ-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of κ-Poincar´e algebra. Several examples of realizations are worked out in details

Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole

We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for quasinormal mode frequencies, the area and entropy spectra for the BTZ black hole in the presence of noncommutativity are calculated. In particular, the separations between the neighboring values of these spectra are determined and it is found that they are nonuniform. Therefore, it appears that the noncommutativity leads to a non-equispaced (discrete) area and entropy spectra.Comment: 11 pages, improved version published in JHE

Toward the classification of differential calculi on κ-Minkowski space and related field theories

Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincar\'e Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications

Carcass Composition of Turopolje Pig, the Autochthonous Croatian Breed

Objective of this research was to establish carcass composition in Turopolje pig breed by analyzing the percentage of muscle (M), fat (F) and bone (B) tissue, percentage of these tissues in different parts of carcass (ham, loin, back, neck, belly-rib part . BRP), as well as share of the parts in carcass. Animals were divided into two groups of different age and slaughtering weight (TI 584 ± 20 days and 81,9 kg; TII 679 ± 20 days and 100,3 kg ± 4,9 kg). Purpose of this investigation was to define the standards for traits mentioned for the remainder of the population of Turopolje pig and to set the selection and production programs, as this breed has been under protection since 1993 and re-establishment since 1996 as cultural and biological heritage of Croatia and the World. In order to define Turopolje pig in production sense, we presented characteristics of the old breeds Mongolitza and Black Slavonian and some selected breeds. Pigs were fattened in the outdoor system of flood forests and marsh meadows biocenosis (Quercus robur . Deschampsietum caespitosae), according to traditional Croatian technology of low input (Ðikić et al., 2002). Slaughtering weight and weight of warm and cold carcass were measured on the slaughtering line. The halves were separately weight and dissected (tissues and parts) according to Weninger et al., 1963 and by total dissection. Data were processed by statistical-mathematical procedure GSM and SAS software package (1996) and results were compared within and between the groups ( t-test). In groups TI and TII the percentages tissues in carcass were established to be as follows: M 38.2% and 40.5%, B 10.6% and 9.7%, respectively, and were significantly different ( P< 0.05), while share of F, 34.2% and 33.8% were not significantly different. Fattened pigs in group TI, in relation to TII, had lower relative share of muscle tissue in the carcass of loin, back, neck and BRP and higher share of fat tissue of neck and BRP, as well as bone tissue of leg and loin. Muscle : fat tissue relation established for groups TI i TII (1.02 :1 and 1.07 :1) are higher than in Mongolitza, but lower than in Black Slavonian pig and selected breed