I couldn't help myself... I had to stop doing homework to write this up, so anyway, here it is. Mashburn's ring. It's bothered me quite a bit for some time (the lack of a solid explanation), so here I go. 

First, we have to take into account what we know. 
1 - His ring is plain and gold. 
2 - He wears his ring on his right hand. 

So, first we have to ask ourselves, what kind of ring is this? http://www.ehow.com/facts_5004268_what-right-hand-ring.html This link explains how to choose a right hand ring and their purpose ("dress ring"). They tend to be elaborate. There doesn't even seem to be an example of a right hand ring that doesn't have a stone. Furthermore, if one were to be very rich (billionaire) a plain gold ring on their right hand would be embarrassing due to its function (dress ring). Bear in mind that Mashburn has been extremely wealthy for ~15 years (ages 30-45). There's no way that he still operates as a freshly wealthy person. He's been in the in crowd for too long to not understand how to dress/decorate himself. We can also consider him someone who is deeply concerned with his personal appearance from 3 pieces of evidence. Jane says he has, "a mild dirt phobia and thinks he sweats two much." Those two things indicate someone who is self conscious. The third thing is that Mashburn is narcissitic, by his own analysis. Those three things in combination with how long he's been rich make it highly unlikely that he doesn't know how to dress/decorate himself. 

So why would an someone who is smart/has been rich for a good while/narcissitic wear a plain cheap wedding ring? Well, because it is a wedding band. Not only does it look like a wedding band, but a man like Walter Mashburn would not be seen wearing a cheap looking band unless it had sentimental value. Here's a link that describes why people wear a wedding ring on their right hand: http://www.ehow.com/facts_5150243_do-wedding-ring-right-hand_.html Among the list are 2 major possibilities: Widowhood, and Left handedness. First I'll explain why I don't consider the other 3 to be viable reasons. Culture: Walter isn't from Greece, India, Poland, etc. He seems to have been living in America for a very long time and is probably very American. Infidelity: Walter isn't married. Gay: It's pretty clear that Walter is heterosexual. Family Heirloom: I do not believe this to be reasonable. First, I don't even know if it applies to male wedding bands. However, we don't know anything about his family history beyond his mother. Furthermore, Walter is new money and I will explain the importance of that later. So we are left with only one real possibility. Although left handedness is quite possible, Walter is not married, so we can't conclude that it SHOULD be on his left hand. So, we can conclude that Walter wore the ring on his right hand because he is still has strong sentiments toward the woman he loved. It is important to note that you don't buy a wedding band the day of your marriage, you buy one when you plan on getting married (engagement). Furthermore, many people like to buy engagement rings with their wedding band so that they can wear them together post marriage. So it makes perfect sense for Walter to pick up the wedding band while buying the wedding band for his fiance. 

So I'd like to stop here and move on to the hooker that I believe wrote, "he is mar." I've written arguments for it being the hooker and for it being "married" before, so I won't waste my time doing it here. If you wish to argue this point, please divert your attention to my theory (1370). So the first point I do want to focus on is, would she consider a ring on his right hand married? Well she is a hooker, and that means she's probably encountered men who are cheating on their wives. One of the six reasons listed for wearing a ring on your right hand was infidelity. It's not unlikely that she's seen men wearing a wedding band on their right hand while they were cheating. Furthermore, she could believe that he was wearing the ring on his right hand because he was left handed, which is also another reason that people wear a wedding ring on their righ thand. Then there's the fact that she wasn't casually examining him, she was being murdered by him. All three of those arguments could explain her declaring a wedding band on the right hand as a statement of marriage. But that's not the only question we have to ask. When was Walter last married? We don't see Walter until season 2 and by then Jared had been killed a year ago. He could have been married when he killed Jared. 

Moving away from the hooker, I want to bring up why Walter took his ring off between s2e13 and s3e7. I'm going to offer all the reasons I can. He didn't want Jane to see it, or because he wanted to try to get Lisbon (not that the ring impaired him before, just that it might be a ticking time bomb if he spent more time around her). He may have lost the need for the ring (it could have been a reminder that of his loss to Yuri) and now he had finally won, he was good enough to take it off. He could have fallen in love with someone else (bear in mind Miranda Martins was killed in 2007 and we first see lorelei in 2012. This means that Mashburn got with her sometime within that timeframe. The question isn't how long would it take him to win her, it's how long would it take her to win him (if this was the case). I do not personally believe that Lorelei could win RJ over, however, I want to point out that she calls RJ out on his, "relentless manipulation," which seems to be something exclusive to her. No one else indicates that RJ has a bad side, except for Roslind calling him cruel for leaving without a trace. It could indicate a number of things, none of which I'm going to comment on, I'll leave it to you. He could have not wanted Yuri to see him wearing the ring that symbolizes his defeat to him (this episode takes place within the time frame of 1-2 days I think, and the final night Walter is seen at a hotel, which might indicate that he stayed in that side of town over night prior to sleeping with Lisbon).
 
It might also be important to note that Mashburn still hates Yuri, after all this time. The fact that he still harbors that type of hate for Yuri indicates two things. One, that he lost a sense of his self worth because he couldn't keep his woman from leaving him for Yuri, and two, that he cares for Mrs. Bajoran (if not, why wouldn't he hate her too for leaving him and why would he harbor such hatred for Yuri if Yuri didn't still have what he wanted [his wife]). Super long sentence... 

Well, that was quite a bit of text, but I'm ready to conclude now. I'll tell you what I think to be the case. I think Mashburn wears the ring because it has sentimental value (similar to Mercedes' promise to Edmond in the Count of Monte Cristo or as a remind to himself that he wasn't good enough to win Mrs. Bajoran), and I think that he didn't wear the ring to see Yuri because he either didn't need to given that he'd finally beat Yuri and redeemed his self worth that he lost with Mrs. Bajoran, or because he didn't want Yuri to potentially see his weakness, especially when it was supposed to be his moment of triumph.