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This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local. To achieve it, we use the theory of generalized functions and the Fourier transform in the space of tempered distributions $\mathcal{S}^\prime$. We show that the non-local operator domain is not defined on the whole functional space but on a subset of it. Moreover, we prove that these functions and their derivatives are bounded in all $\mathbb{R}^3$ and, consequently, the Riemann tensor is regular and the scalar curvature invariants do not present any spacetime singularity. Finally, we explore what conditions we need to satisfy so that the solutions of the linearized equations of motion exist in $\mathcal{S}^\prime$., 23 pages, comments welcome!

We present a new bouncing cosmological solution of the non-local theory known as infinite derivative gravity, which goes beyond the recursive ansatz, ${\Box R = r_1 R +r_2}$. The non-local field equations are evaluated using the spectral decomposition with respect to the eigenfunctions of the wave operator. The energy-momentum tensor computed for this geometry turns out to be much more sensitive to the choice of the non-local form-factor, since it depends on the value of the function on a continuous infinite interval. We show that this stronger dependence on the form-factor allows us to source the geometry by the perfect fluid with the non-negative energy density satisfying the strong energy condition. We show that this bouncing behaviour is not possible in the local theories of gravity such as in general relativity or $R+R^2$ gravity sourced by a fluid which meets the non-negative energy and strong energy conditions., Comment: 12 pages

We solve the non-local equation ${-e^{-\ell^2\square}\square{\phi}=J}$ for i) static scalar fields in static spacetimes and ii) time-dependent scalar fields in ultrastatic spacetimes. Corresponding equations are rewritten as non-local Poisson/inhomogeneous Helmholtz equations in compact and non-compact weighted/Riemannian manifolds using static/frequency-domain Green's functions, which can be computed from the heat kernels in the respective manifolds. With the help of the heat kernel estimates, we derive the static Green's function estimates and use them to discuss the regularity. We also present several examples of exact and estimated static/frequency-domain Green's functions., Comment: 19 pages, 6 figures, comments welcome!

U ovom radu prikazan je postupak određivanja visina točaka geodetske osnove u parku Jelenovac u Zagrebu, a koja se koristi za potrebe praktične nastave na kolegijima Geodetskog fakulteta Sveučilišta u Zagrebu. Nakon pripremnih radova, kao što je rekognosciranje terena i planiranje opažanja, obavljena je izmjera geodetske osnove primjenom metoda geometrijskog, trigonometrijskog i GNSS nivelmana. Nakon inicijalne obrade, provedeno je izjednačenje geodetske osnove, u konvencionalnom i optimalnom datumu, na osnovi podataka geometrijskog i trigonometrijskog nivelmana. Dobivene su višestruke konačne vrijednosti visina točaka i pripadne ocjene točnosti te je provedena analiza dobivenih rezultata. Visine točaka dobivene geometrijskim nivelmanom uzete su za referentne vrijednosti.

We formulate several criteria under which the symmetries associated with the Killing and Killing-Yano tensors on the base space can be lifted to the symmetries of the full warped geometry. The procedure is explicitly illustrated on several examples, providing new prototypes of spacetimes admitting such tensors. In particular, we study a warped product of two Kerr-NUT-(A)dS spacetimes and show that it gives rise to a new class of highly symmetric vacuum (with cosmological constant) black hole solutions that inherit many of the properties of the Kerr-NUT-(A)dS geometry., 10 pages, no figures

We study spacetimes that lead to a separable Klein-Gordon equation in a general dimension. We introduce an ansatz for the metric in higher dimensions motivated by analogical work by Carter in four dimensions and find solutions of the Klein-Gordon equation. For such a metric we solve the Einstein equations and regain the Kerr-NUT-(A)dS spacetime as one of our results. Other solutions lead to the Einstein-K\"ahler metric of a Euclidean signature. Next we investigate a warped geometry of two Klein-Gordon separable spaces with a properly chosen warped factor. We show that the resulting metric leads also to a separable Klein--Gordon equation and we find the corresponding solutions. Finally, we solve the Einstein equations for the warped geometry and obtain new solutions., Comment: 12 pages, no figures

We investigate properties of higher-dimensional generally rotating black-hole spacetimes, so called Kerr-NUT-(A)dS spacetimes, as well as a family of related spaces which share the same explicit and hidden symmetries. In these spaces, we study a particle motion in the presence of a weak electromagnetic field and compare it with its operator analogies. First, we find general commutativity conditions for classical observables and for their operator counterparts, then we investigate a fulfillment of these conditions in the Kerr-NUT-(A)dS and related spaces. We find the most general form of the weak electromagnetic field compatible with the complete integrability of the particle motion and the comutativity of the field operators. For such a field we solve the charged Hamilton-Jacobi and Klein-Gordon equations by separation of variables., Comment: 12 pages, 0 figures

Four children are presented with Class II pancreas injury as a result of a motor vehicle accident. The first child was taken to the operating room promptly due to concomitant perforation of the hollow viscus (gastric rupture) and underwent successful spleen-sparing distal pancreatectomy with preservation of the splenic artery and vein. The next three cases with isolated abdominal symptoms of pancreatic injury generally experienced a delay of one day before the onset of abdominal symptoms and positive diagnostic investigation results and were managed non-operatively (NOM) on admission ; they were then treated surgically due to developing peritonitis after 24, 36, and 38 hours, respectively. The same type of operation, even though delayed and technically much more demanding, was performed, but this was not an obstacle to our efforts to preserve the spleen and its full circulation, in order to provide full immunological and haematological support during the expected prolonged postoperative course. We did not lose any of the children. A reintervention was needed in two children due to the retention of necrotic tissue and intraabdominal abscess. The serum amylase level in all cases remained above normal. We believe that a spleen-preserving distal pancreatectomy with splenic vessel conservation can be safely performed, even in delayed operations, and should be indicated for the surgical management.

Presented are the cases of 19 boys with ventral penile curvature without hypospadias. The cases were categorised into three groups according to the severity of the anomaly. In group I were 7 boys with ventral penile curvature affecting the shortening of the frenulum with skin tethering. The anomaly was corrected by fraenulotomy and, in 4 boys, by ventral "V" and "Y" penile skinplasty with excellent cosmetic results. In group II were 10 boys with an evident chordee. In 4 boys, the chordee was of type III according to Devin-Horton. A chordectomy was done with a "V" and "Y" skinplasty with very good result. The remaining 6 cases were chordee type II according to D-H. The same treatment was undertaken here, but with an additional Nesbit's dorsal tunica albuginea plication in 4 boys and a 50% success (3 of 6). In group III were 5 boys, 3 previously failed chordectomy from group II and 2 with "skin urethra" type chordee I according to D-H. All boys in this group were treated for urethroplasty with autologous buccal mucosal graft. Good results were obtained in 3 of 5 (60%). Successful outcome was achieved in both cases with "skin urethra" not previously treated. The results of our urethroplasty with buccal mucosa agree with those in literature. In the treatment of chordee without hypospadias, where it was necessary to reconstruct the urethra there was a constant problem of the shortage of local tissue, so we believe that buccal mucosa is a good choice.

Retrospektivno je prikazan razvoj Traumatološkog odjela Opće bolnice Zabok u razdoblju od 1983. - 1998. godine, uz iznošenje osnovnih statističkih podataka o stručnoj djelatnosti iz područja traumatologije u Krapinsko-zagorskoj županiji., The paper is a retrospective review of the Traumatology Ward at the Zabok General Hospital in the period 1983-1998. The basic statistical data on the expertise in traumatology in Krapinsko-zagorska County are presented.