The Theory of Pseudo-Radiation Local Emitt ers Value of Properties with a Diff erential Propagation of Prices Wave**

The shape property value of each segment is a function of resultant vectors corresponding factors price-determining. Estimation structural coeffi cients of the analytic model, confi rmed by empirical value parameters stochastic, shows the deterministic importance location in the context of their value. Problem distribution prices in space was and is the subject of many direct or indirect scientifi c discussions, among others [1–3, 6, 15, 10, 12–14, 16], but in era permanently increasing real estate prices do not continue its topicality. Current knowledge in fi le property valuation led to the conclusion, that the level value is the highest in the center and decreases towards periphery. The author of this thesis rightly also notes that in larger cities can be clearly identify, outside the main center city, district centers [8]. They may cause, that radiation propagation of prices wave, transmitt ed as it were by a single emitt er (city center) is refracted coexistence districts center with strong interference extreme. The statement so, that prices drop is not uniform; shapes it because system main arterial roads in the city and places their intersection with trade and service centers of second or third row [5] is over-generalization phenomenon spectral distribution prices. This was a solid foundation for the study, the aim of which was to verify the original theory of propagation of wave prices. In its outline the authors accept the assumption, that on a right-area real estate market exist at least two emitt ers prices, so points, on which unit prices rising (emitt ers progressive) or decrease (emitt ers regressive) in pseudo-radial. By this, we mean not uniform changes in prices in relation to the allocation of real estate in monitored space of variable development trends. It is further assumed, that wave prices propagated by progressive emitt ers have a lower amplitude and frequency vibration, while transmitted through regressive emitt ers are characterized by high beginning frequency and a strong damping vibrations in the fi rst phase with parallel relatively high amplitude. This study does not take research emitt ers price other than a point, despite the fact that both linear (along roads, tram lines etc.) and superfi cial (around airports, parks etc.) in the authors opinion share rules propagation of wave prices of a point emitt ers.


Methodology of Verifi cation Conception
The licensed professional group responsible for estimating property value are real estate appraisers.In part of good practice, they should reach out for new, often even innovation technological solutions, guaranteeing acquisition information not only about subject evaluation, but also about structure right-subject real estate market.As we read in International Valuation Standards: real estate appraiser should have access to advanced systems of collecting information [9].One of them is the Geographic Information System.It allows considering distribution property prices in space not only with quantitative data, as done before, but also basis on visual interference.IVSC point out, that use GIS to valuation real estates is recommended and should become common practice [4].
In view of dynamic development algorithms property valuation, which is accompanied by not slower fl owering possibilities Geography Information System, both fi elds applied to verify theory of pseudo-radiation local emitt ers property values with assuming diff erential propagation wave prices.
As test material was adopted data about real estate premises located in Krakow, available for free portal OpenStreetMap.Their preparation was made in open structure QGIS, implementing OSM plugin allows download suitable layers of geoinformation about apartments.SpatiaLite base was established basis on topology stored in fi le ".osm".Finally, test material concentrated in shapefi le fi le, thus allowing for a comparison of algorithms estimating wave prices in free QGIS application with commercial ArcGIS.
Verifi cation of pseudo-radiation local emitt ers property values consists in taking district centers, where are observed extreme prices.In the theory assumed cause, that propagation transmitt ed wave prices is neither steady nor uniform trends.Therefore, research pseudo-radiation involves the falsifi cation thesis stipulating, that real estate value is the highest in the center and decreases in periphery direction [8] without indirect changes tendency of fl uctuation of property prices.So, should take at least one emitt er regressive and one progressive.Then simulate wave radiation emanating throughout the monitored area.Wavelength should be equal, but allowed its increase or reduction in order to maintain a relatively coincident with number test data (describe off er prices) falling within the scope (λ i ).For purpose, this analysis is taken as test data the off er prices.In separate studies the authors of this research show, that in monitored space "negotiation fi led" at an around of 5%.In progress, this study is planned a complete change off er prices on transaction prices.
Test conception brought so to generate appropriate buff er around local emitt ers, which have been established in form rings of predefi ne dimeter and the beginning ring (r b,i ) is expressed in formula: while (r e,i ) is complement the initial limit circle (r b,i ) of length i-th wave (λ i ) and is given by model: Construction spatial query for objects, whose centroid is located within the (i-th) wave radiation, allows its scope (λ i ) set: -number residential (l i ), -minimum unit price (c i,min ), -maximum unit price (c i,max ), -average unit price (ˆi c ), -variance unit prices ( 2 i ).Variance in this case should be identifi ed fi rst and foremost with diversity market characteristic of real estates including falling within a singles wave prices, because shape unit price is a function of many variables, not only location, for the assuming arbitrarily, but with high probability is the most deterministic.
The theory of pseudo-radiation local emitt ers' value of properties is appropriate, when analytic function approximating average unit prices (ˆi c ) is not monotonic, i.e. when for regressive emitt ers there is no condition (3), and for progressive there is no condition (4): Diff erential propagation wave prices occur, when    ˆ( ) 0 i i c diff erence dispersion coeffi cient averages unit prices from neighboring waves length λ i and λ i + 1 is not equal diff erence dispersion coeffi cient another pairs at total length emitt ing wave λ i+1 + λ i+2 .Diff erential wave in the author's theory is so fulfi lled fallowing relation: or: Process estimation real estate values is saddled factors, which cannot be included in valuation models, which have a negative impact on accuracy result.It should also be emphasized, that value is derived from prices resulting from the game of supply and demand, so changing vary dynamic.

Inaccuracy estimation makes the diff erential equation emission wave prices:
is unatt ainable in realities free market.Thus, fulfi llment of condition ( 7) is considered the situation: The theory of pseudo-radiation local emitt ers' value of properties with a diff erential propagation of prices wave subjected to also visual reasoning the correctness assumptions.Based on unit prices of apartments, distributed evenly throughout the area of the analyzed market, was interpolated pseudo wave prices used triangulated irregular network (TIN), which vertices correspond to pointwise deployed off er prices.Tools to constrain TIN and interpolation of pseudo wave prices provides environmental QGIS as well as ArcGIS.As an alternative to triangulated irregular network was selected interpolation wave, describe analyzed occurrence by nearest neighbor method (in ArcGIS) and the method of inverse distance (in QGIS and ArcGIS).It is recognized, that the author's theory is true in terms pseudo-radiation local emitt ers of property values, when of propagation waves due to existing more than one emitt er, and everyone transmitt ed a signal-prices variously in each direction them propagation.Maintain the theory in part of diff erential propagation wave prices is observation diff erence speed increase or decrease off er unit prices between regressive and progressive emitt ers, as manifested by frequency signifi cant change level these prices.

Empirical Presentation the Conception
The test material including apartments located in Krakow and belonging administratively to districts: Śródmieście, Krowodrza -the eastern part, Nowa Hutathe western part, Podgórze -the northern part.By sample, kriging [11] established for them two regressive emitt ers: "Rynek Główny" and "Wola Justowska" as well as one progressive emitt er named "Podgórze".Kriging results coincide with a real view perception of the market among local society [7].In ArcGIS environmental was simulated the process of radial propagation wave prices for varying length (λ i ).Their autonomic propagation is shown in Figure 1 with signature (+) localization representative properties od established off er prices.
To verify the theory of pseudo-radiation local emitt ers' value of properties with a diff erential propagation of prices wave used ArcGIS statistics (juxtaposition in Tables 1-3) consolidation for all emitt ers and integrated it with single plane cross-section of average prices observed in the individual waves.Average unit prices of apartments, on analysis property market, exhibit high variability in successive waves transmitt ed radially form emitt ers.Based on juxtaposed in Tables 1-3 results derive conclusion, that regressive emitt ers accompanied greater and faster change of prices in early phase propagation than progressive emitters.Evidenced by the diff erence between and ."Podgórze" because emits waves of extreme volatility in level 1 341.68PLN/m 2 , "Rynek Główny" and "Wola Justowska" in levels, accordingly 2 984.84 PLN/m 2 and 3 146.07PLN/m 2 .These mean, that on the analyzed market are large areas of lower, but stable prices and are opposite for the less numerous apartments in prestige districts.Based on the obtained empirical results maintain in entirety thesis, that propagation emits wave prices is not uniform and not of homogenous development trends.Not uniform revealed a lack of harmonized diff erences averages unit prices observed in neighboring waves.It is also cause not homogenous development trends, because transmission price signal from emitters "Rynek Główny" and "Wola Justowska" does not correspond with equation (3).Progressive emitt er "Podgórze" moreover is not subject to equation (4).Quantitative data confi rmed in Tables 1-3, which in the last columns visualization single plane cross-section of wave prices.It shows, that volatility off er prices of apartments is not monotonic, especially in the case adopted as an authoritative source signal emitt er "Wola Justowska".
As a result comparison dispersion coeffi cients , with accepted 5% tolerance mismatch, it is stated fulfi llment condition (6).These mean, that also true is the conception in part on diff erential propagation wave prices.
The conducted research allows for the conclusion, that imbalance variance depends mainly on the distance of emitt ed wave prices relative to the emitt er.The larger diameter in case radiation propagation, in wave range included more diverse real estates, i.e. with diff erent functional or technical parameters or localization advantages.For example is composition wave of length λ 8 = 500 m, away from the emitter "Rynek Główny" 3 500 m, included both extreme expensive properties located in Wola Justowsja as well as minimalistic apartments (in border analyses market) locate in districts Nowa Huta (western part) and Podgórze (northern part).In such a contrast regions dominate diametric types of real estates, with diff erent standard, workmanship, surrounding and others market characteristics.That anomalies lower quality estimation averages unit prices in range individual waves, which is mapped in relative high variance prices.The aim of increasing accuracy analyzes planes to transition from off er prices to transaction prices contained in notarial acts.This will also reduce specifi c characteristics technical-functional real estates from peeled segment market.
Enriching quantitative assessment, the theory is visual assessment study area for detection potential emitt ers wave prices, because it was assumed they polycentric existing and diff erential propagation caused by allocation epicenters prices in medium disturbed (emitt ers interact witch each other).
Below are presented the visualization of propagation waves based on: -triangulated irregular network (Fig. 2), realized in the environmental ArcGIS and QGIS, -nearest neighbor method (Fig. 3), realized in the environmental ArcGIS, -inversed distance method (Fig. 4), realized in the environmental ArcGIS and QGIS.

Conclusions
On the pages of this study presented the theory of pseudo-radiation local emitters' value of properties with a diff erential propagation of prices wave.Gathered test material from Krakow's real estate market applies apartments, proved multitude polarizers prices with bipolar specify signal transmission.Can distinguish regressive emitt ers, relatively easy to identify by the nearest neighbor method (available in ArcGIS) and triangulated irregular network (available in ArcGIS and QGIS).Can distinguish also progressive emitt ers, which interpolation is hinders stabilization lower level of prices in a wide area analyses.Pseudo-radiation of polarizers has been proved by reveal lack monotonicity of distribution of off er unit prices observed in individual waves with variable lengths.Proven also, that is the appropriate understanding variable prices in waves as a diff erential succession uncorrelated their levels in multifactorial (poly-polarization) medium spectral, because the diff erence between dispersion coeffi cient tangent waves (compared in pairs), and imposed a 5% tolerance mismatch, do not equal.It has been shown, that early speed of signal propagation from regressive emitt ers, in the fi rst phase growing the fastest, but further is strong suppressed.Progressive emitt ers are more stable.Price waves are limited lower amplitude, which refl ected in small variability prices and less sensitive to extreme regions (districts).
In conclusion, the research process, sustain entirely the author's theory of pseudo-radiation local emitt ers' value of properties with a diff erential propagation of price waves.The authors also recognize the possibility of further development through equalization representative properties describe market characteristics and transaction prices as well as linking taken issue with rules of mechanic distribution waves on water mirror.Theory proposed by the authors is basis for further analysis aimed at creating idea to modeling market or cadastral values of real estates in any market segment.

Table 1 .
Summary parameters to verify monotonic and diff erential wave prices for regressive emitt er named "Rynek Główny"

Table 2 .
Summary parameters to verify monotonic and diff erential wave prices for regressive emitt er named "Wola Justowska" Tabela 3. Summary parameters to verify monotonic and diff erential wave prices for progressive emitt er named "Podgórze"