On the existence of some ARCH(∞\infty) processes

A new sufficient condition for the existence of a stationary causal solution of an ARCH($\infty$) equation is provided. This condition allows to consider polynomially decaying coefficients, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved

SOVIETŲ SĄJUNGOS PAVELDAS – POKYČIŲ BEIEŠKANT

Recenzij

Ietigalis sidabru inkrustuota įmova iš Vilkijos

Spearheads decorated with precious and other nonferrous metals are rare finds in Baltic territories. One of them was uncovered by chance in Vilkija (Kaunas district, Lithuania) during soil cultivation works in the autumn of 2000. This was a lanceolate spearhead with a silver encrusted socket.This article is designed to publish the mentioned find, determine its chronology and origin, and review other spearheads with inlayed sockets uncovered in the Baltic territories.The Vilkija spearhead is 22.2 cm long with a 3.2 cm wide lanceolate blade and 2.4 cm diameter silver encrusted socket (Fig. 1). The ornament of the socket represents a horizontally striped composition. It is an arrangement of two similarly patterned stripes composed of 4 recurring “loop” motifs. The design is a geometrical plait of loops interconnected by a stripe interweaved through tabs. It is made by a deep line with opposing notches composing the herring-bone motif (Fig. 1:3).In the material culture of the Baltic tribes, 44 spearheads with sockets encrusted with silver and other nonferrous metals are known. They are of 5 types: III, IVb, E, G and K (according to J. Petersen, 1919 and A. Ruttkay, 1976). The most numerous ones are spearheads of type III (17 items) followed by IVb and E (7 each), G (6) and K (4) (Table 1). The type of one spearhead has not been identified.All these spearheads are decorated with ornaments of three types: 1) geometrical; 2) runic; and 3) striped-weaved or Prussian (Fig. 6).The ornaments of geometrical style are based on strictly geometrical motifs: narrow, horizontal, silver and copper stripes engirdling the sockets, zigzag lines, net and herring-bone motifs, combinations of small prolonged or step-like rhombuses (Fig. 2, 3, 4:2, 3). Sometimes the ornaments of this group are combinations of a few motifs. The lower parts of the sockets often have wider stripes with a more expressive design composed of zigzag or net motifs (Fig. 3). The rest of the socket is decorated with horizontal lines (Fig. 2).The runic ornaments arc based on winding, interweaved lines designed to fom1 fantastic figures (Fig. 4).The striped-weaved or Prussian ornaments arc based on a striped composition of plaits of loops interconnected by a stripe interweaved through tabs (Fig. 5, 6:3). The motif’s of such ornaments are arranged in one, two, three or four lines. The Vilkija spearhead should be ascribed to group 3 (Fig. 6:3).Many spearheads with inlayed sockets have been found with items of richly furnished burials. For this reason they can be rather precisely dated. Moreover, the typological analysis of blade forms and socket ornaments is also chronologically informative. The furnishings of burials – ornaments, other kinds of weapons and riding gear – revealed that spearheads with silver – inlayed sockets are mostly found with “Curonian” type brooches, M type axes, axes with the blade prolonged toward the blunt end, T type, saddle-shaped (type XV; according to A. Ruttkay, 1976) or oval knobs swords, sword chapes belonging to type IV (according to V. Kazakevičius, 1976), stirrups of types III, IV and VII (according to J. Antanavičius, 1976), spurs of types I and III (according to A. Н. Kирпичников, 1973), dirhams and Byzantine coins and other chronologically not well identified items of riding gear as, for example, riding bits, bindings of bridle belts and buckles. All listed artefacts are widespread in the Baltic territory and are virtually dated to the 11th century.It is more difficult to date the spearheads according to their typology. Armourers have constantly sought the most rational forms, size and proportion of spearheads. The spearheads which best answered the military requirements would be rapidly and widely adopted and used for a long time. Therefore, very precise dating is difficult. However, it is obvious that spearheads of types III, IVb, E and G were most widespread and popular among the warriors of the Baltic tribes in the 11th century. The imported K type European spearheads are also dated to the 11th century. The socket ornament of spearheads may serve as a good chronological indicator, particularly if it was widespread and well studied as is the runic type of ornaments. It appeared in Scandinavia in the 11th century and took root in the decorations of various material cultures archeological artefacts. The geometrical ornament is known in different parts of Scandinavia (more widespread in Gotland), Norway, Finland and Estonia.According to the well dated burial items and analogues from Western Europe, the striped-weaved (Prussian) ornament distinguished by the author as typical for the Baltic lands should also be dated to the 11th century. Judging from the burial items and the ornamentation and typology of the spearheads, their use was limited to the 11th century. For this reason, the Vilkija spearhead with a silver – inlayed socket also may be dated to the 11th century and traced to the Prussian lands

Dėl E tipo ietigalių ornamentuotomis įmovomis chronologijos ir kilmės

Weapons have always been in the focus of attention of European archaeologists. As early as the beginning of 20th century several monographs were written which haven’t yet lost their importance and may be renderred among the classics of archaeological science. However, it must be admitted that the number of studies devoted to the most abounding type of weapons of the Iron Age – spears – is still insufficient. This is especially true about the spearheads found in the territory occupied by Baltic tribes. Investigators of Baltic tribes archaeology cannot boast of capital works or somewhat more exhaustive studies on spears. Only a few articles and chapters of some generalizing works are known which, however, are too short and abstract to satisfy the researchers specializing in certain types of weapons.This article devoted to a particular purpose: to discuss the problems of chronology and origin of E type (according to J. Petersen) spearheads with ornamented sockets from the Viking period.Two subtypes of E – type spearheads are found in the Baltic archaeological sites from the Viking period. Some of them have ornamented other ones – plain (without ornaments) sockets (Fig. 1). The ornament is composed of grooves arranged along the socket into arched lines which are brought together into one spot near the blade. On the opposite end these grooves form several arches (Fig. 2). This ornament is differently called by various authors: arched, Gothic, flame-shaped. It, presumably, serves only as a decoration and is not related with manufacturing technologies.Spearheads without decorated sockets make the absolute majority, whereas, those with arched-line ornament belongs to rarer finds. According to the available data 56 such spearheads were found in 26 archaeological sites (Fig. 3). Taking into consideration the present state and administrative boundaries 34 items were found in Lithuania, 6 – in Latvia and 16 E – type spearheads with decorated sockets found in the territory of former East Prussia. The given number might be not precise because it is difficult to count the finds from the East Prussia due to the lack of reliable data: records and literature. The largest number of such weapons – 14 – was uncovered in the Kaup bei Wiskiauten barrow cemetery. In other archaeological sites they were sparser: 5 spearheads in 4 graves of Upyna burial ground (Šilalė district), 4 – in Kretuonys barrow cemetery (Švenčionys district) (Fig. 9), 3 – in the Kapiņu Kristapēni burial ground (Preiladistrict), 2 spearheads in each were found in the Čiobiškis (Širvintos district) barrow cemetery, Marvelė (Kaunas) and Palanga burial grounds. It was a rare case when the Rupunionys (Kaunas district) hoards of weapons yielded two E – type spearheads with ornamented sockets (Fig. 4). In other Baltic archaeological sites such spearheads were uncovered isolated (Fig. 11) or stray finds (Fig. 5). The find spots of some other spearheads are not known.Not only ornaments but other weapons as well, uncovered in the same graves, are important in determining the chronology of E – type spearheads. These weapons include 196 swords, other types of spears, shield bosses and battle knives (1, 2 Tables). E – type spearheads with sockets decorated in arched-line ornament were found together with swords in 14 graves (Table 1). The H – type swords – found in 4 cases – were the most frequent finds. They were followed by V – type swords – in 3 graves – and swords of types B, E, K, M, Y, X – one find of each type. The B type sword is one of the earliest types of swords in the Viking period. It was found together with the discussed type of spearhead in grave No 124 (195) of Laiviai (Kretinga district) burial ground. In the Baltic territories these swords are dated to the end of 18th–9th C. A. D.Grave No 151a of Kaup bei Wiskiauten barrow cemetery which yielded a K – type sword with other artefacts (Fig. 6) is dated to the middle of 9th century. Graves from the 9th–10th centuries yielded also H, M, and Y types of swords. The latest E – type spearheads with ornamented sockets were uncovered in Kaup bei Wiskiauten and Palanga together with V and X types of swords and other artefacts (Fig. 7, 8).Among the ornaments which help to date the sets o(finds including the E – type socketed spearheads the most frequent are brooches: penannular with rolled, quadrangle and faceted terminals, sometimes ladder and cross-bow brooches with popy-head terminals, in rare cases – tortoise-shaped. “Warrior’s” bracelets serve as a good chronological indicator as well (Fig. 10).Thus, the archaeological material indicates that E – type socketed spearheads were included in the Baltic weaponry within the years 800–1050. At the beginning of 11th century such spearheads were rare exceptions.As to the origin of the E – type spearheads in the areas occupied by Balts there is an almost common oppinion that they came from Scandinavian lands where they were rather popular. Such oppinion is substantiated by archaeological data and circumstances of uncovering of these weapons. They prove that manufacturing centres of such weapons were situated in Scandinavia.As all imported weapons the E – type spearheads were very expensive and they did not play the role of “democratic” weapon in the Baltic weaponry. Not all members of society armed with such spearheads. They were possessed only by well-armed warriours. The statistical average of the set of weapons revealed that warriours possessing the E – type spearheads were also armed with a sword and another spear. Thus, we may conclude that E – type spearheads, as also swords, were included into the weaponry of professional warriours, i.e., persons who belonged to nobility

Dėl E tipo ietigalių ornamentuotomis įmovomis chronologijos ir kilmės

Weapons have always been in the focus of attention of European archaeologists. As early as the beginning of 20th century several monographs were written which haven’t yet lost their importance and may be renderred among the classics of archaeological science. However, it must be admitted that the number of studies devoted to the most abounding type of weapons of the Iron Age – spears – is still insufficient. This is especially true about the spearheads found in the territory occupied by Baltic tribes. Investigators of Baltic tribes archaeology cannot boast of capital works or somewhat more exhaustive studies on spears. Only a few articles and chapters of some generalizing works are known which, however, are too short and abstract to satisfy the researchers specializing in certain types of weapons.This article devoted to a particular purpose: to discuss the problems of chronology and origin of E type (according to J. Petersen) spearheads with ornamented sockets from the Viking period.Two subtypes of E – type spearheads are found in the Baltic archaeological sites from the Viking period. Some of them have ornamented other ones – plain (without ornaments) sockets (Fig. 1). The ornament is composed of grooves arranged along the socket into arched lines which are brought together into one spot near the blade. On the opposite end these grooves form several arches (Fig. 2). This ornament is differently called by various authors: arched, Gothic, flame-shaped. It, presumably, serves only as a decoration and is not related with manufacturing technologies.Spearheads without decorated sockets make the absolute majority, whereas, those with arched-line ornament belongs to rarer finds. According to the available data 56 such spearheads were found in 26 archaeological sites (Fig. 3). Taking into consideration the present state and administrative boundaries 34 items were found in Lithuania, 6 – in Latvia and 16 E – type spearheads with decorated sockets found in the territory of former East Prussia. The given number might be not precise because it is difficult to count the finds from the East Prussia due to the lack of reliable data: records and literature. The largest number of such weapons – 14 – was uncovered in the Kaup bei Wiskiauten barrow cemetery. In other archaeological sites they were sparser: 5 spearheads in 4 graves of Upyna burial ground (Šilalė district), 4 – in Kretuonys barrow cemetery (Švenčionys district) (Fig. 9), 3 – in the Kapiņu Kristapēni burial ground (Preiladistrict), 2 spearheads in each were found in the Čiobiškis (Širvintos district) barrow cemetery, Marvelė (Kaunas) and Palanga burial grounds. It was a rare case when the Rupunionys (Kaunas district) hoards of weapons yielded two E – type spearheads with ornamented sockets (Fig. 4). In other Baltic archaeological sites such spearheads were uncovered isolated (Fig. 11) or stray finds (Fig. 5). The find spots of some other spearheads are not known.Not only ornaments but other weapons as well, uncovered in the same graves, are important in determining the chronology of E – type spearheads. These weapons include 196 swords, other types of spears, shield bosses and battle knives (1, 2 Tables). E – type spearheads with sockets decorated in arched-line ornament were found together with swords in 14 graves (Table 1). The H – type swords – found in 4 cases – were the most frequent finds. They were followed by V – type swords – in 3 graves – and swords of types B, E, K, M, Y, X – one find of each type. The B type sword is one of the earliest types of swords in the Viking period. It was found together with the discussed type of spearhead in grave No 124 (195) of Laiviai (Kretinga district) burial ground. In the Baltic territories these swords are dated to the end of 18th–9th C. A. D.Grave No 151a of Kaup bei Wiskiauten barrow cemetery which yielded a K – type sword with other artefacts (Fig. 6) is dated to the middle of 9th century. Graves from the 9th–10th centuries yielded also H, M, and Y types of swords. The latest E – type spearheads with ornamented sockets were uncovered in Kaup bei Wiskiauten and Palanga together with V and X types of swords and other artefacts (Fig. 7, 8).Among the ornaments which help to date the sets o(finds including the E – type socketed spearheads the most frequent are brooches: penannular with rolled, quadrangle and faceted terminals, sometimes ladder and cross-bow brooches with popy-head terminals, in rare cases – tortoise-shaped. “Warrior’s” bracelets serve as a good chronological indicator as well (Fig. 10).Thus, the archaeological material indicates that E – type socketed spearheads were included in the Baltic weaponry within the years 800–1050. At the beginning of 11th century such spearheads were rare exceptions.As to the origin of the E – type spearheads in the areas occupied by Balts there is an almost common oppinion that they came from Scandinavian lands where they were rather popular. Such oppinion is substantiated by archaeological data and circumstances of uncovering of these weapons. They prove that manufacturing centres of such weapons were situated in Scandinavia.As all imported weapons the E – type spearheads were very expensive and they did not play the role of “democratic” weapon in the Baltic weaponry. Not all members of society armed with such spearheads. They were possessed only by well-armed warriours. The statistical average of the set of weapons revealed that warriours possessing the E – type spearheads were also armed with a sword and another spear. Thus, we may conclude that E – type spearheads, as also swords, were included into the weaponry of professional warriours, i.e., persons who belonged to nobility

Verslo įmonių finansinių ataskaitų analizė

Šioje mokomojoje knygoje išaiškinami verslo įmonių finansinių ataskaitų pokyčiai, nagrinėjami nauji finansinių ataskaitų rinkiniai, atskleidžiami šių rinkinių analizės ypatumai bei jų įtaka finansinei analizei atlikti. Skaitytojui pateikiamos ir pagrindinės finansinės analizės teorijos žinios, naudotinos verslo įmonių finansinių ataskaitų analizėje. Mokomojoje knygoje pateikiama finansinių ataskaitų analizės metodika, kuri pasiteisino praktinėje autorių analitinėje veikloje, konsultuojant verslo įmones bei diegiant jose finansinės analizės sistemas. Taip pat pateikiami siūlymai, kaip sistemiškai spręsti įmonių finansinės analizės informacinio aprūpinimo klausimus, dirbant su naujos formos finansinėmis ataskaitomis, kaip taikyti populiariausius finansinės analizės būdus, naudojantis šiuolaikinėmis informacinėmis technologijomis

An approach to 24-hour electrocardiogram monitoring in sheep experimental model

Sheep could be an excellent research subject for large animal experimental studies because of their heart structure and physiology have a lot similarity to the human. Long term ECG monitoring is a convenient tool for human and possibly veterinary clinical practice and research. Continuous ECG recording can be used to monitor and evaluate body physiological responses in various experimental conditions. Experience on sheep ECG monitoring techniques is sparse and mostly focused on short term ECG recordings. We developed a peculiar technique of 24-hour sheep ECG monitoring based on the available data on large mammal model, where we tried to share some insights and practical solutions working with this type of animals for ECG monitoring by using several commercially available ECG monitors also used for the human practice. Some producer specific hardware and software characteristic that we found important in daily practice were also discussed. In conclusion, sheep as big animal is relatively good object for Holter monitoring experimental studies: ECG monitoring is easily affordable, registered ECG signal is of similar quality as in human clinical practice, which is sufficient for the heart rhythm monitoring and arrhythmia and conduction disorder diagnostics. Additional effort might be needed for 24-hour heart rate variability calculations because manual revision of software ECG signal interpretations is requiring, but short-term calculations can be made easy

Non-parametric estimation from simultaneous renewal–failure–degradation data with competing risks

A new joint model for linear degradation and competing failure data with partial renewals is proposed. Non-parametric statistical estimation procedures for failure intensities and failure probabilities as functions of degradation level are given