Pulsed-laser generation of gold nanoparticles with on-line surface plasmon resonance detection

Size of nanoparticles is an important parameter for their applications. The real-time monitoring is required for reliable and reproducible production of nanoparticles with controllable size. We present results of our research on development of the system for the online nanoparticle characterization during their production by a laser. The laser ablation chamber which allows measurements of surface plasmon resonance spectra during the nanoparticle generation process has been designed and fabricated. The online characterization system was tested by producing and modification of gold nanoparticles. Nanoparticles were generated by nanosecond-laser (wavelength 1064 nm) ablation of gold target in deionized water, and optimal conditions for the highest nanoparticle productivity were estimated. The mean diameter of nanoparticles was determined using their absorption spectra measured in the real-time during the ablation experiments and from the TEM images analysis, and it varied from 20 to 45 nm. The mismatch between nanoparticle diameters, estimated using these two methods, is due to the polydispersity of the generated nanoparticles. The further experiments of laser-induced modification of colloidal gold nanoparticles were carried out using second harmonic (wavelength 532 nm) of nanosecond Nd:YAG laser and alteration in nanoparticle size were acquired by the online measurement system.     

Preferred Attachment in Affiliation Networks

Vertices of an affiliation network are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop (or video-sharing website) are called adjacent if they have purchased (or downloaded) the same or similar items. Assuming that each newly arrived customer is linked preferentially to already popular items we obtain a preferred attachment affiliation network that evolves in time. We show that the fraction of customers having \(i\) neighbours scales as \(i^{-2-\alpha }\ln i\) for large \(i\) . Here \(\alpha >0\) is the ratio between the two intensities: intensity of the flow of customers and that of the newly arriving items.     

A Berry-Esseen bound for least squares error variance estimators of regression parameters

We construct a precise Berry-Esseen bound for the least squares error variance estimators of regression parameters. Our bound depends explicitly on the sequence of design variables and is of the order O(N ^−1/2) if this sequence is “regular” enough. Supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 1–8, January–March, 1999.     

Formulation of Ocular In Situ Gels with Lithuanian Royal Jelly and Their Biopharmaceutical Evaluation In Vitro

Royal jelly is a natural substance produced by worker bees that possesses a variety of biological activities, including antioxidant, anti-inflammatory, antibacterial, and protective. Although fresh royal jelly is kept at low temperatures, to increase its stability, it needs to be incorporated into pharmaceutical formulations, such as in situ gels. The aim of this study was to formulate in situ ocular gels containing Lithuanian royal jelly for topical corneal use in order to increase the retention time of the formulation on the ocular surface and bioavailability. Gels were evaluated for physicochemical characteristics (pH, rheological properties, refractive index) and in vitro drug release measuring the amount of 10-hydroxy-2-decenoic acid (10-HDA). An ocular irritation test and cell viability tests were performed using the SIRC (Statens Seruminstitut Rabbit Cornea) cell culture line. Results indicated that all the in situ gels were within an acceptable pH and refractive index range close to corneal properties. Rheology studies have shown that the gelation temperature varies between 25 and 32 °C, depending on the amount of poloxamers. The release studies have shown that the release of 10-HDA from in situ gels is more sustained than royal jelly suspension. All gel formulations were non-irritant according to the short-time exposure test (STE) using the SIRC cell culture line, and long-term cell viability studies indicated that the formulations used in small concentrations did not induce cell death. Prepared in situ gels containing royal jelly have potential for ocular drug delivery, and they may improve the bioavailability, stability of royal jelly, and formation of non-irritant ocular formulations.     

Development and Validation of the UPLC-DAD Methodology for the Detection of Triterpenoids and Phytosterols in Fruit Samples of Vaccinium macrocarpon Aiton and Vaccinium oxycoccos L.

Cranberries are used in the production of medicinal preparations and food supplements, which highlights the importance of triterpene compounds determination in cranberry fruit raw material. The aim of our study was to develop and validate for routine testing suitable UPLC-DAD methodology for the evaluation of triterpene acids, neutral triterpenoids, phytosterols, and squalene content in cranberry samples. The developed and optimized UPLC-DAD methodology was validated according to the guidelines of the International Council for Harmonization (ICH), evaluating the following parameters: range, specificity, linearity (R² > 0.999), precision, LOD (0.27–1.86 µg/mL), LOQ (0.90–6.18 µg/mL), and recovery (80–110%). The developed and validated technique was used for the evaluation of triterpenic compounds in samples of Vaccinium macrocarpon and Vaccinium oxycoccos fruits, and their peels, pulp and seeds. The studied chromatogram profiles of Vaccinium macrocarpon and Vaccinium oxycoccos were identical but differed in the areas of the analytical peaks. Ursolic acid was the dominant compound in fruit samples of Vaccinium macrocarpon and Vaccinium oxycoccos. The highest amounts of triterpenic compounds were detected in the cranberry peels samples. The developed method for the detection of triterpene compounds can be applied in further studies for routine testing on the qualitative and quantitative composition of fruit samples of Vaccinium macrocarpon and Vaccinium oxycoccos species and cultivars.     

A random intersection digraph: Indegree and outdegree distributions

Let S(1),…,S(n),T(1),…,T(n) be random subsets of the set [m]={1,…,m}. We consider the random digraph D on the vertex set [n] defined as follows: the arc i→j is present in D whenever S(i)∩T(j)≠0?. Assuming that the pairs of sets (S(i),T(i)), 1≤i≤n, are independent and identically distributed, we study the in- and outdegree distributions of a typical vertex of D as n,m→∞.     

A Berry-Esséen bound for student's statistic in the non-I.I.D. case

We establish a Berry-Esséen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esséen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.Research supported by the SFB 343 in Bielefeld.     

On the distribution of the norm for a multidimensional Brownian bridge

Vilnius University. Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 1, pp. 30–39, January–March, 1991.     

Central limit theorem for stochastically continuous processes. Convergence to stable limit

LetX={X(t), t[0, 1]} be a stochastically continuous cadlag process. Assume that thek dimensional finite joint distributions ofX are in the domain of normal attraction of strictlyp-stable, 0<p<2, measure onR ^k for all 1k<. For functionsf, g such that _p (|X(x–X(u)|) >g(u–s) and _p (|X(s–X(t|)|X(t)–X(u|)>f(u–s), 0 s t u 1, conditions are found which imply that the distributions –(n ^–1/p (X ₁+···+X _n )),n1, converge weakly inD[0, 1] to the distribution of ap-stable process. HereX ₁,X ₂, ... are independent copies ofX and _p (Z)=sup _t<0 t ^pP{|Z|<t} denotes the weakpth moment of a random variable Z.