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The spectrum of one-dimensional repulsive Hamiltonian with a class of perturbations $H_p=-\frac{d^2}{dx^2}-x^2+V(x)$ in $L^p(\R)$ ($1 p$. Additionally, non-existence of related Schr\"odinger ($C_0$-)semigroup in $L^p(\R)$ is shown when $V(x)\equiv 0$.

This paper deals with the solvability in the semilinear abstract evolution equation with countable time delays, \begin{document}$ \begin{equation*} \begin{cases} \dfrac{du}{dt}(t)+Au(t) = F(u(t), (u(t-\tau_n))_{n\in\mathbb{N}}), & t>0, \\ u(t) = u_0(t), & t \in \bigcup\limits_{n \in \mathbb{N}}[-\tau_n,0], \end{cases} \end{equation*} $\end{document} in a Banach space \begin{document}$ X $\end{document}, where \begin{document}$ -A $\end{document} is a generator of a \begin{document}$ C_0 $\end{document}-semigroup with exponential decay and \begin{document}$ F: X \times X^\mathbb{N} \to X $\end{document} is Lipschitz continuous. Nicaise and Pignotti (J. Evol. Equ.; 2018;18;947–971) established global existence and exponential decay in time for solutions of the above equation with finite time delays in Hilbert spaces under global or local Lipschitz conditions. The purpose of the present paper is to generalize the result to the case of countable time delays in Banach spaces under a global Lipschitz condition.

This paper deals with the initial-boundary value problem (denoted by (CGL) ) for the complex Ginzburg–Landau type equation ∂ u ∂ t − ( λ + i α ) Δ u + ( κ + i β ) | u | q − 1 u − γ u = 0 with initial data u 0 ∈ L p ( Ω ) in the case 1 q 1 + 2 p / N , where Ω is bounded or unbounded in R N , λ > 0 , α , β , γ , κ ∈ R . There are a lot of studies on local and global existence of solutions to (CGL) including the physically relevant case q = 3 and κ > 0 . This paper gives existence results with precise properties of solutions and rigorous proof from a mathematical point of view. The physically relevant case can be considered as a special case of the results. Moreover, in the case κ 0 , local and global existence of solutions with the decay estimate ‖ u ( t ) ‖ L p ( Ω ) ≤ c 1 e − c 2 t ( c 1 , c 2 are positive constants) is obtained under some conditions. The key to the local existence is to construct a semigroup { e t [ ( λ + i α ) Δ ] } and its L p - L q estimate. On the other hand, the key to the global existence is to derive estimates for solutions by using a kind of interpolation inequality with Re 〈 | v | p − 2 v , − ( λ + i α ) Δ v 〉 .

This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation $$ \dfrac {\partial u}{\partial t} -(\lambda +{\rm i} \alpha )\Delta u +(\kappa +{\rm i} \beta )|u|^{q-1}u-\gamma u=0 $$ in $\mathbb {R}^{N}\times (0,\infty )$ with $L^{p}$-initial data $u_{0}$ in the subcritical case ($1\leq q 0$, $p>1$, ${\rm i} =\sqrt {-1}$ and $N\in \mathbb {N}$. The proof is based on the $L^{p}$-$L^{q}$ estimates of the linear semigroup $\{\exp (t(\lambda +{\rm i} \alpha )\Delta )\}$ and usual fixed-point argument.

A new existence and uniqueness theorem is established for linear evolution equations of hyperbolic type with strongly measurable coefficients in a separable Hilbert space. The result is applied to the Dirac equation with time-dependent potential.

This paper is concerned with Cauchy problems for the linear Schrodinger evolution equation (i(∂/∂t) + Δ + |x – a(t)|–1 + V1(x,t))u(x,t) = f(x,t) in RN × [0,T], subject to initial condition: u(·,0) ∈ H2(RN) ∩ H2(RN), where i := $\sqrt{-1}$, N ≥ 3, T > 0 and a : [0,T] → RN expresses the center of the Coulomb potential, V1 and f are another real-valued potential and an inhomogeneous term, respectively, while H2(RN) := {v ∈ L2(RN); |x|2v ∈ L2(RN)}. We show that under some conditions on V1 and f the equation has a classical solution u(·) ∈ C1([0,T]; L2(RN)) ∩ C([0,T]; H2(RN) ∩ H2(RN)).

This paper is concerned with the Cauchy problem for the complex Ginzburg-Landau type equation $u_t = (\delta _{1}+i\delta _{2})\Delta u -i\mu |u| ^{2\sigma}u$ in $(0,\infty)\times\mathbb{R}^d$, where $\delta_{1}>0$, $\delta_{2}, \mu \in \mathbb{R}$ and $d\in\mathbb{N}$. Existence and uniqueness of spatially periodic solutions to the problem are established in a space which corresponds to the Sobolev space on the $d$-dimensional torus when $0

The sub-genomic replicon of tick-borne encephalitis (TBE) virus (Far-Eastern subtype) was packaged into infectious particles by providing the viral structural proteins in trans. Sequential transfection of TBE replicon RNA and a plasmid that expressed the structural proteins led to the secretion of infectious particles that contained TBE replicon RNA. The secreted particles had single-round infectivity, which was inhibited by TBE virus-neutralizing antibody. The physical structure of the particles was almost identical to that of infectious virions, and the packaged replicon RNA showed no recombination with the mRNAs of the viral structural proteins. Furthermore, heterologous genes were successfully delivered and expressed by packaging TBE replicon RNA with inserted GFP and Neo genes. This replicon packaging system may be a useful tool for the molecular study of the TBE virus genome packaging mechanism, and for the development of vaccine delivery systems.

Phylogenetic analysis of tick-borne encephalitis (TBE) virus revealed that Hokkaido strain of TBE virus evolved several hundreds years ago in far-east Russia. TBE virus strains in Irkutsk area were identified as Siberian subtype of TBE virus. BHK-cell adapted mutant of TBE virus showed lower neuro-invasive virulence in mice than parent virus. The mutant carried one amino acid substitution in envelope protein which resulted in increase of positive charge of the protein. The mutant-infected mice showed lower virus titers in bloods and spleens than the parent-infected mice. Infectious c-DNA clone of TBE virus Hokkaido strain was successfully generated and was applied to examine the neurovirulence in mice. One amino acid change in envelope protein and 2 amino acid changes in Ns5 protein showed a synergistic effect on reduced neurovirulence in mice.

Flaviviruses are assembled to bud into the lumen of the endoplasmic reticulum (ER) and are secreted through the vesicle transport pathway. Virus envelope proteins play important roles in this process. In this study, the effect of mutations in the envelope proteins of tick-borne encephalitis (TBE) virus on secretion of virus-like particles (VLPs), using a recombinant plasmid expression system was analysed. It was found that a single point mutation at position 63 in prM induces a reduction in secretion of VLPs. The mutation in prM did not affect the folding of the envelope proteins, and chaperone-like activity of prM was maintained. As observed by immunofluorescence microscopy, viral envelope proteins with the mutation in prM were scarce in the Golgi complex, and accumulated in the ER. Electron microscopic analysis of cells expressing the mutated prM revealed that many tubular structures were present in the lumen. The insertion of the prM mutation at aa 63 into the viral genome reduced the production of infectious virus particles. This data suggest that prM plays a crucial role in the virus budding process.

A stable full-length infectious cDNA clone of the Oshima strain of Tick-borne encephalitis virus (Far-Eastern subtype) was developed by a long high-fidelity RT-PCR and one-step cloning procedure. The infectious clone (O-IC) had four amino acid substitutions and produced smaller plaques when compared with the parent Oshima 5-10 strain. Using site-directed mutagenesis, the substitutions were reverted to restore the parent virus sequence (O-IC-pt). Although genetically identical, parent virus Oshima 5-10 and virus recovered from O-IC-pt demonstrated some biological differences that are possibly explained by the presence of quasispecies with differing virulence characteristics within the original virus population. These observations may have implications for vaccines based on modified infectious clones. It was also demonstrated that the amino acid substitution E-S40→P at position 40 in the envelope (E) glycoprotein was responsible for plaque size reduction, reduced infectious virus yields in cell culture and reduced mouse neurovirulence. Additionally, two amino acid substitutions in the non-structural (NS)5 protein (virus RNA-dependent RNA polymerase) NS5-V378→A and NS5-R674→K also contributed to attenuation of virulence in mice, but did not demonstrate a noticeable biological effect in baby hamster kidney cell culture. Comparative neurovirulence tests revealed how the accumulation of individual mutations (E-S40→P, NS5-V378→A and NS5-R674→K) can result in the attenuation of a virus.

We derived the baby hamster kidney (BHK)-21 cell culture-adapted, tick-borne encephalitis (TBE) virus mutant. To reveal the pathogenicity of the TBE virus, we compared the pathogenicity of the mutant (Oshima Cl-1) and parental (Oshima 5-10) virus in mouse model. The neurovirulence of mutant in mice was identical to that of parent. However, the level of neuroinvasiveness was higher for parent than for mutant. The degrees of viremia and virus titers in the spleen were lower in mice that were inoculated subcutaneously (s.c.) with mutant than in mice that received parent. Unlike parent, mutant was rarely detected in the brains of s.c. inoculated mice. Genetic analysis revealed that mutant had single amino acid substitutions in each of the E and NS5 proteins compared with parent. Furthermore, while mutant infection of BHK-21 cells was inhibited by glycosaminoglycans (GAGs), this was not the case for parent. In summary, the BHK-21-cell-adapted mutant virus showed reduced neuroinvasiveness in mice due to low-level induction of viremia. The attenuation process involved a single amino acid change in the E protein, which may have resulted in the rapid clearance of the virus due to its high affinity for negatively charged molecules in vivo.

A recombinant plasmid that expresses the tick-borne encephalitis (TBE) virus premembrane (prM) and envelope (E) proteins in mammalian cells was constructed. Recombinant proteins retained antigenic and conformational structures similar to those of native virus proteins, and transfected cells released virus-like particles (VLPs), which were 1.13–1.14 g/ml in density and 20–30 nm in diameter, into the culture medium. Recombinant E proteins were used for the development of an enzyme-linked immunosorbent assay (ELISA) to detect TBE virus-specific IgM and IgG antibodies in serum. The results of this ELISA correlated well with the results of commercial ELISA, when tested with 95 serum samples from clinically TBE-suspected patients. In addition, ELISA using recombinant antigens showed no cross-reactivity against serum from Japanese encephalitis (JE) patients, despite the cross-reactivity shown by commercial ELISA systems. These observations indicated that this newly developed ELISA system could distinguish tick-borne encephalitis from Japanese encephalitis infection, and that it constitutes a useful and safe alternative to conventional ELISA systems.

The tick-borne encephalitis (TBE) virus has two membrane glycoproteins (prM and E), which each has one N-linked glycan. Constructs that express prM and E proteins of TBE virus have been shown to produce virus-like particles (VLPs), which have surface properties that are similar to those of infectious viruses. To reveal the function of glycosylation of the TBE virus prM and E proteins in the secretion of VLPs, we expressed glycosylation-mutated prM and E proteins and compared the secretion levels and biological properties of the VLPs. In the prM protein glycosylation-deficient mutant, the level of secreted E protein was reduced to 60% of the wild-type level. On the other hand, in the E or prM-E protein glycosylation-deficient mutant, the level of secreted E protein was reduced to 10% of the wild-type level. Furthermore, the mutant which was glycosylated at positions 66 and 154 in protein E, the level of secreted E protein was four-fold higher than that of the wild-type. However, in the mutant which was glycosylated at position 66 only, E protein secretion was reduced to only 10% of the wild-type level. These data suggest that the glycan associated with the N-linked glycosylation site at position 154 in protein E plays an important role in VLP secretion.

We constructed three sub-genomic replicons of Tick-borne encephalitis virus (TBEV) (Oshima REP, Oshima REP-GFP and Oshima REP-Neo) by deleting genes coding for structural proteins without or with insertion of green fluorescent protein (GFP) or Neo genes, respectively. BHK cells transfected with Oshima REP expressed the viral non-structural antigens in immunofluorescent and western blot analyses. GFP and viral antigens were co-expressed in the transfected cells with Oshima REP-GFP. G418-resistant cells harboring Oshima REP-Neo consistently expressed the antigens without showing any apparent CPE. These replicons constructed in this study will be useful in studies on the replication, assembly and packaging of TBEV, and to develop vaccines and gene-delivering systems.

We compared the biological properties of Oshima 5-10 (tick-borne encephalitis [TBE] virus isolated in Hokkaido, Japan) and Sofjin-HO (Far-Eastern subtype TBE virus) including plaque formation, virus replication and virus protein synthesis in BHK-21 cell cultures to reveal strain differences. We also determined the complete nucleotide sequences of both strains and compared the deduced amino acid sequences. Plaques of Oshima 5-10 were smaller than those of Sofjin-HO. Virus titers in culture fluid of Oshima 5-10 were 1/100 of those of Sofjin-HO at 9 and 12 hr after infection. Less viral protein and RNA syntheses of strain Oshima 5-10 was observed than with Sofjin-HO. Genetic analysis revealed 1.4% of amino acids to differ with Sofjin-HO. No difference between the two strains was detected in the motif sequence of the viral enzyme, cleavage sites of viral protein or glycosylation sites of NS1.

To evaluate the efficacy of the European TBE vaccine in east-Siberian and far-eastern regions of Russia, we examined the immune responses of the vaccine against recent TBE virus Siberian (Irkutsk) and far-eastern (Khabarovsk and Vladivostok) isolates. The sera of vaccinated humans showed efficient neutralizing antibody titers (> or =20) against Siberian and far-eastern strains. To evaluate the efficacy of the vaccine in vivo, mice were vaccinated and challenged with lethal doses of the viruses. All vaccinated mice survived each virus challenge. These results suggest that the European vaccine can prevent the TBE virus infection in east-Siberian and far-eastern regions of Russia.